BACKGROUND Panic disorder(PD)involves emotion dysregulation,but its underlying mechanisms remain poorly understood.Previous research suggests that implicit emotion regulation may play a central role in PD-related emot...BACKGROUND Panic disorder(PD)involves emotion dysregulation,but its underlying mechanisms remain poorly understood.Previous research suggests that implicit emotion regulation may play a central role in PD-related emotion dysregulation and symptom maintenance.However,there is a lack of studies exploring the neural mechanisms of implicit emotion regulation in PD using neurophysiological indicators.AIM To study the neural mechanisms of implicit emotion regulation in PD with eventrelated potentials(ERP).METHODS A total of 25 PD patients and 20 healthy controls(HC)underwent clinical evaluations.The study utilized a case-control design with random sampling,selecting participants for the case group from March to December 2018.Participants performed an affect labeling task,using affect labeling as the experimental condition and gender labeling as the control condition.ERP and behavioral data were recorded to compare the late positive potential(LPP)within and between the groups.RESULTS Both PD and HC groups showed longer reaction times and decreased accuracy under the affect labeling.In the HC group,late LPP amplitudes exhibited a dynamic pattern of initial increase followed by decrease.Importantly,a significant group×condition interaction effect was observed.Simple effect analysis revealed a reduction in the differences of late LPP amplitudes between the affect labeling and gender labeling conditions in the PD group compared to the HC group.Furthermore,among PD patients under the affect labeling,the late LPP was negatively correlated with disease severity,symptom frequency,and intensity.CONCLUSION PD patients demonstrate abnormalities in implicit emotion regulation,hampering their ability to mobilize cognitive resources for downregulating negative emotions.The late LPP amplitude in response to affect labeling may serve as a potentially valuable clinical indicator of PD severity.展开更多
This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones a...This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.展开更多
BACKGROUND People with bipolar disorder(BD)frequently struggle with the recurrence of affective symptoms.However,the interplay between coping mechanism and positive mood state remains under-researched.AIM To explore t...BACKGROUND People with bipolar disorder(BD)frequently struggle with the recurrence of affective symptoms.However,the interplay between coping mechanism and positive mood state remains under-researched.AIM To explore the associations among behavioral approach system(BAS)sensitivity level,coping,and positive mood states among people with BD.METHODS Using a cross-sectional study design,90 participants with BD were presented with four BAS-activating life event scenarios and assessed with regard to their BAS trait sensitivity,coping flexibility,and mood states.A hierarchical clustering method was used to identify different groups with different styles of coping.Multiple hierarchical regression analyses were conducted to examine the mediating and moderating roles of different components of coping on mood states.RESULTS A three-cluster solution was found to best fit the present data set.The findings showed that a low mass of coping combined with low BAS sensitivity level protects people with BD from detrimentally accentuating mood states when they encounter BAS-activating life events.Moreover,coping flexibility is demonstrated to mediate and moderate the relationships between BAS sensitivity level and mood states.Specifically,subduing the perceived controllability and reducing the use of behavioral-activation/emotion-amplifying coping strategies could help buffer the effect of positive affect.CONCLUSION The judicious use of coping in emotion regulation for people with BD when encountering BAS-activating life events was indicated.Practical applications and theoretical implications are highlighted.展开更多
An end-effector for a flexible drilling robot is designed, and a novel four-point algorithm of normal attitude regulation for this end-effector is presented. Four non-coplanar points can define a unique sphere tangent...An end-effector for a flexible drilling robot is designed, and a novel four-point algorithm of normal attitude regulation for this end-effector is presented. Four non-coplanar points can define a unique sphere tangent to them in spatial geometry, and the center point of the sphere and the radius can be calculated. The shape of a workpiece surface in the machining area is approximately regarded as such a sphere. A vector from the machining point to the center point is thus approximately regarded as a normal vector to the workpiece surface. By this principle, the algorithm first measures four coordinates on the curve in the drilling region using four sensors and calculates the normal vector at the drilling point, then calculates the error between the normal vector and the axis of the spindle. According to this error, the algorithm further figures out the angles of two revolving axes on the end- effector and the displacements of three linear axes on the robot main body, thus it implements the function of adjusting the spindle to be perpendicular to the curve at the drilling point. Simulation results of two kinds of curved surfaces show that accuracy and efficiency can be realized using the proposed algorithm.展开更多
By removing panicles and spikelets, the effects of nitrogen supply-demand balance(NSDB)on nitrogen translocation and senescence of leaves at different positions of the same stem in rice plant were studied. The results...By removing panicles and spikelets, the effects of nitrogen supply-demand balance(NSDB)on nitrogen translocation and senescence of leaves at different positions of the same stem in rice plant were studied. The results showed that under NSDB<0(CK), nitrogen translocation and senescence of the top 4 leaves was normal. Nitrogen exported from the top leaves(LFT)especially the top 4 leaves decreased remarkably with increase of NSDB. thus, their MDA contents and differences in color(SPAD value)decreased, while the activities of SOD and CAT increased. Under NSDB>0(panicle removal), N accumulation of the top 4 leaves increased significantly, and the leaf senescence process was delayed. The results also indicated that the color of the 4th LFT was mainly affected by NSDB among the top 4 leaves and was lighter than the 3rd LFT when nitrogen supply was insufficient for the sink need.展开更多
In this article, we consider the existence of two positive solutions to nonlinear second order three-point singular boundary value problem: -u′′(t) = λf(t, u(t)) for all t ∈ (0, 1) subjecting to u(0) = ...In this article, we consider the existence of two positive solutions to nonlinear second order three-point singular boundary value problem: -u′′(t) = λf(t, u(t)) for all t ∈ (0, 1) subjecting to u(0) = 0 and αu(η) = u(1), where η ∈ (0, 1), α ∈ [0, 1), and λ is a positive parameter. The nonlinear term f(t, u) is nonnegative, and may be singular at t = 0, t = 1, and u = 0. By the fixed point index theory and approximation method, we establish that there exists λ* ∈ (0, +∞], such that the above problem has at least two positive solutions for any λ ∈ (0, λ*) under certain conditions on the nonlinear term f.展开更多
An existence theorem of positive solution is established for a nonlinear third-order three-point boundary value problem. Here, we concentrated on the case that the nonlinear term is neither superlinear nor sublinear, ...An existence theorem of positive solution is established for a nonlinear third-order three-point boundary value problem. Here, we concentrated on the case that the nonlinear term is neither superlinear nor sublinear, and is not asymptotic at zero and infinity.展开更多
In this paper,we study the existence of triple positive solutions for the nonlinear third-order three-point boundary value problem ■where η∈[0,1/2) is a constant,by using a fixed-point theorem due to Avery and Pete...In this paper,we study the existence of triple positive solutions for the nonlinear third-order three-point boundary value problem ■where η∈[0,1/2) is a constant,by using a fixed-point theorem due to Avery and Peterson,we establish results of triple positive solutions to the boundary value problem,and an example is given to illustrate the importance of result obtained.展开更多
In this paper, we consider the positive solutions of fractional three-point boundary value problem of the form Dο^α+u(t)+f(t,u(t),u'(t),…,u^(n-3)(5),u^(n-2)(t))=0,u^(i)(0)=0,0≤i≤n-2,u^(n-...In this paper, we consider the positive solutions of fractional three-point boundary value problem of the form Dο^α+u(t)+f(t,u(t),u'(t),…,u^(n-3)(5),u^(n-2)(t))=0,u^(i)(0)=0,0≤i≤n-2,u^(n-2)(1)-βu^(n-2)(ξ)=0,where 0〈t〈1,n-1〈α≤n,n≥2,ξ Е(0,1),βξ^a-n〈1. We first transform it into another equivalent boundary value problem. Then, we derive the Green's function for the equivalent boundary value problem and show that it satisfies certain properties. At last, by using some fixed-point theorems, we obtain the existence of positive solution for this problem. Example is given to illustrate the effectiveness of our result.展开更多
In this paper, we consider existence of single or multiple positive solutions of three-point boundary value problems involving one-dimensional p-Laplacian. We then study existence of solutions when the problems are in...In this paper, we consider existence of single or multiple positive solutions of three-point boundary value problems involving one-dimensional p-Laplacian. We then study existence of solutions when the problems are in resonance cases. The proposed approach is based on the Krasnoselskii's fixed point theorem and the coincidence degree.展开更多
In this paper, we study the existence of positive solutions for a class of third-order three-point boundary value problem. By employing the fixed point theorem on cone, some new criteria to ensure the three-point boun...In this paper, we study the existence of positive solutions for a class of third-order three-point boundary value problem. By employing the fixed point theorem on cone, some new criteria to ensure the three-point boundary value problem has at least three positive solutions are obtained. An example illustrating our main result is given. Moreover, some previous results will be improved significantly in our paper.展开更多
In this paper, we consider the three-point boundary value problem (φp(uˊˊ(t)))ˊ +a(t)f(t, u(t), uˊ(t), uˊˊ(t)) = 0, t ∈ [0, 1] subject to the boundary conditions u(0) =βuˊ(0), uˊ(1) =...In this paper, we consider the three-point boundary value problem (φp(uˊˊ(t)))ˊ +a(t)f(t, u(t), uˊ(t), uˊˊ(t)) = 0, t ∈ [0, 1] subject to the boundary conditions u(0) =βuˊ(0), uˊ(1) = αuˊ(η), uˊˊ(0) = 0, where φp(s) = |s|p?2s with p 〉 1, 0 〈 α, η 〈 1 and 0 ≤ β 〈 1. Applying a fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions to the above boundary value problem.展开更多
The existence of positive solutions is established for a nonlinear second-order three-point boundary value problem. The result improves and extends the main result in Electron J. Differential Equations, 34(1999), 1-8.
Married female adolescents are the most vulnerable people that culturally marry with their parents’ permission in Iran. This study aimed to investigate the effectiveness of stress inoculation training (SIT) on cognit...Married female adolescents are the most vulnerable people that culturally marry with their parents’ permission in Iran. This study aimed to investigate the effectiveness of stress inoculation training (SIT) on cognitive emotional regulation (CER) in these women. The method of this research was semi-experiment with pretest and posttest. The statistical society was the married adolescent female students from Qom high schools (80 people). First, they were assessed by cognitive emotional regulation questionnaire to find the subjects under the CER cut of point (55 people). Then 30 participants were randomly selected and were equally divided into experimental and control groups. The entry criteria for samples were female married students between 17 and 19 from low socioeconomic income. The experimental group received 8 sessions of SIT training while there was no intervention for control group. Results from MANCOVA analysis showed that there were significant differences between groups on cognitive emotional regulation in post-test. The data of pretest were the covariate factor. Finding suggests SIT is effective for cognitive emotional regulation in vulnerable married female adolescents. In addition, this training method elevates positive emotional strategies, which correlate with planning, focusing and organizing the emotions. In contrast, except self and the others blaming, negative emotional strategies differed slightly.展开更多
In this paper, the second-order three-point boundary value problem u(t) + λa(t)f(t, u(t)) = 0, 0 < t < 1,u(t) = u(1- t), u(0)- u(1) = u(12)is studied, where λ is a positive parameter, under various assumption ...In this paper, the second-order three-point boundary value problem u(t) + λa(t)f(t, u(t)) = 0, 0 < t < 1,u(t) = u(1- t), u(0)- u(1) = u(12)is studied, where λ is a positive parameter, under various assumption on a and f, we establish intervals of the parameter λ, which yield the existence of positive solution, our proof based on Krasnosel'skii fixed-point theorem in cone.{u"(t)+λa(t)f(t,u(t))=0,0<t<1,u(t)=u(1-t),u′(0)-u′(1)=u(1/2)is studied,where A is a positive parameter,under various assumption on a and f,we establish intervals of the parameter A,which yield the existence of positive solution,our proof based on Krasnosel'skii fixed-point theorem in cone.展开更多
By using the Krasnoselskii's fixed point theorem for cones,conditions for the existence of positive solutions to the three-point boundary value problem for second order differential equation with an advanced argum...By using the Krasnoselskii's fixed point theorem for cones,conditions for the existence of positive solutions to the three-point boundary value problem for second order differential equation with an advanced argumentu″(t)+λa(t)f(u(h(t)))=0, t∈(0,1), u(0)=0, αu(η)=u(1),where 0<η<1,0<α<1η and t≤h(t)≤1 are obtained.展开更多
This paper is devoted to the study of the existence and uniqueness of the positive solution for a type of the nonlinear third-order three-point boundary value problem. Our results are based on an iterative method and ...This paper is devoted to the study of the existence and uniqueness of the positive solution for a type of the nonlinear third-order three-point boundary value problem. Our results are based on an iterative method and the Leray-Schauder fixed point theorem.展开更多
In this paper, the existence of monotone positive solution for the following secondorder three-point boundary value problem is studied:x″(t)+f(t,x(t))=0,0〈t〈1,x′(0)=0,x(1)+δx′(η)=0,where η ∈ (...In this paper, the existence of monotone positive solution for the following secondorder three-point boundary value problem is studied:x″(t)+f(t,x(t))=0,0〈t〈1,x′(0)=0,x(1)+δx′(η)=0,where η ∈ (0, 1), δ∈ [0, ∞), f ∈ C([0, 1] × [0, ∞), [0, ∞)). Under certain growth conditions on the nonlinear term f and by using a fixed point theorem of cone expansion and compression of functional type due to Avery, Anderson and Krueger, sufficient conditions for the existence of monotone positive solution are obtained and the bounds of solution are given. At last, an example is given to illustrate the result of the paper.展开更多
Using the method of lower and upper solutions, we study the following singular nonlinear three-point boundary value problems: , where K ∈ C[0,1] ,0 α η < 1 and λ is a positive parameter and present the existenc...Using the method of lower and upper solutions, we study the following singular nonlinear three-point boundary value problems: , where K ∈ C[0,1] ,0 α η < 1 and λ is a positive parameter and present the existence, uniqueness, and the dependency on parameters of the positive solutions under various assumptions. Our result improves those in the previous literatures.展开更多
In this paper, we investigate the existence of positive solutions for a singular third-order three-point boundary value problem with a parameter. By using fixed point index theory, some existence, multiplicity and non...In this paper, we investigate the existence of positive solutions for a singular third-order three-point boundary value problem with a parameter. By using fixed point index theory, some existence, multiplicity and nonexistence results for positive solutions are derived in terms of different values of λ.展开更多
基金Supported by The National Natural Science Foundation of China,No.81871080the Key R&D Program of Jining(Major Program),No.2023YXNS004+2 种基金the National Natural Science Foundation of China,No.81401486the Natural Science Foundation of Liaoning Province of China,No.20170540276the Medicine and Health Science Technology Development Program of Shandong Province,No.202003070713.
文摘BACKGROUND Panic disorder(PD)involves emotion dysregulation,but its underlying mechanisms remain poorly understood.Previous research suggests that implicit emotion regulation may play a central role in PD-related emotion dysregulation and symptom maintenance.However,there is a lack of studies exploring the neural mechanisms of implicit emotion regulation in PD using neurophysiological indicators.AIM To study the neural mechanisms of implicit emotion regulation in PD with eventrelated potentials(ERP).METHODS A total of 25 PD patients and 20 healthy controls(HC)underwent clinical evaluations.The study utilized a case-control design with random sampling,selecting participants for the case group from March to December 2018.Participants performed an affect labeling task,using affect labeling as the experimental condition and gender labeling as the control condition.ERP and behavioral data were recorded to compare the late positive potential(LPP)within and between the groups.RESULTS Both PD and HC groups showed longer reaction times and decreased accuracy under the affect labeling.In the HC group,late LPP amplitudes exhibited a dynamic pattern of initial increase followed by decrease.Importantly,a significant group×condition interaction effect was observed.Simple effect analysis revealed a reduction in the differences of late LPP amplitudes between the affect labeling and gender labeling conditions in the PD group compared to the HC group.Furthermore,among PD patients under the affect labeling,the late LPP was negatively correlated with disease severity,symptom frequency,and intensity.CONCLUSION PD patients demonstrate abnormalities in implicit emotion regulation,hampering their ability to mobilize cognitive resources for downregulating negative emotions.The late LPP amplitude in response to affect labeling may serve as a potentially valuable clinical indicator of PD severity.
文摘This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.
文摘BACKGROUND People with bipolar disorder(BD)frequently struggle with the recurrence of affective symptoms.However,the interplay between coping mechanism and positive mood state remains under-researched.AIM To explore the associations among behavioral approach system(BAS)sensitivity level,coping,and positive mood states among people with BD.METHODS Using a cross-sectional study design,90 participants with BD were presented with four BAS-activating life event scenarios and assessed with regard to their BAS trait sensitivity,coping flexibility,and mood states.A hierarchical clustering method was used to identify different groups with different styles of coping.Multiple hierarchical regression analyses were conducted to examine the mediating and moderating roles of different components of coping on mood states.RESULTS A three-cluster solution was found to best fit the present data set.The findings showed that a low mass of coping combined with low BAS sensitivity level protects people with BD from detrimentally accentuating mood states when they encounter BAS-activating life events.Moreover,coping flexibility is demonstrated to mediate and moderate the relationships between BAS sensitivity level and mood states.Specifically,subduing the perceived controllability and reducing the use of behavioral-activation/emotion-amplifying coping strategies could help buffer the effect of positive affect.CONCLUSION The judicious use of coping in emotion regulation for people with BD when encountering BAS-activating life events was indicated.Practical applications and theoretical implications are highlighted.
基金National Science and Technology Major Project(No.2009ZX04014-023)
文摘An end-effector for a flexible drilling robot is designed, and a novel four-point algorithm of normal attitude regulation for this end-effector is presented. Four non-coplanar points can define a unique sphere tangent to them in spatial geometry, and the center point of the sphere and the radius can be calculated. The shape of a workpiece surface in the machining area is approximately regarded as such a sphere. A vector from the machining point to the center point is thus approximately regarded as a normal vector to the workpiece surface. By this principle, the algorithm first measures four coordinates on the curve in the drilling region using four sensors and calculates the normal vector at the drilling point, then calculates the error between the normal vector and the axis of the spindle. According to this error, the algorithm further figures out the angles of two revolving axes on the end- effector and the displacements of three linear axes on the robot main body, thus it implements the function of adjusting the spindle to be perpendicular to the curve at the drilling point. Simulation results of two kinds of curved surfaces show that accuracy and efficiency can be realized using the proposed algorithm.
基金supported by the Jiangsu Key Project of Science and Technology(BE2001331)National Key Project of Science and Technology,China(2002BA516A1).
文摘By removing panicles and spikelets, the effects of nitrogen supply-demand balance(NSDB)on nitrogen translocation and senescence of leaves at different positions of the same stem in rice plant were studied. The results showed that under NSDB<0(CK), nitrogen translocation and senescence of the top 4 leaves was normal. Nitrogen exported from the top leaves(LFT)especially the top 4 leaves decreased remarkably with increase of NSDB. thus, their MDA contents and differences in color(SPAD value)decreased, while the activities of SOD and CAT increased. Under NSDB>0(panicle removal), N accumulation of the top 4 leaves increased significantly, and the leaf senescence process was delayed. The results also indicated that the color of the 4th LFT was mainly affected by NSDB among the top 4 leaves and was lighter than the 3rd LFT when nitrogen supply was insufficient for the sink need.
基金supported by the National Natural Science Foundation of China (11071149, 10771128)the NSF of Shanxi Province (2006011002, 2010011001-1)
文摘In this article, we consider the existence of two positive solutions to nonlinear second order three-point singular boundary value problem: -u′′(t) = λf(t, u(t)) for all t ∈ (0, 1) subjecting to u(0) = 0 and αu(η) = u(1), where η ∈ (0, 1), α ∈ [0, 1), and λ is a positive parameter. The nonlinear term f(t, u) is nonnegative, and may be singular at t = 0, t = 1, and u = 0. By the fixed point index theory and approximation method, we establish that there exists λ* ∈ (0, +∞], such that the above problem has at least two positive solutions for any λ ∈ (0, λ*) under certain conditions on the nonlinear term f.
文摘An existence theorem of positive solution is established for a nonlinear third-order three-point boundary value problem. Here, we concentrated on the case that the nonlinear term is neither superlinear nor sublinear, and is not asymptotic at zero and infinity.
基金The National Natural Science Foundation of China(11661071)
文摘In this paper,we study the existence of triple positive solutions for the nonlinear third-order three-point boundary value problem ■where η∈[0,1/2) is a constant,by using a fixed-point theorem due to Avery and Peterson,we establish results of triple positive solutions to the boundary value problem,and an example is given to illustrate the importance of result obtained.
基金Supported by the National Nature Science Foundation of China(11071001)Supported by the Key Program of Ministry of Education of China(205068)
文摘In this paper, we consider the positive solutions of fractional three-point boundary value problem of the form Dο^α+u(t)+f(t,u(t),u'(t),…,u^(n-3)(5),u^(n-2)(t))=0,u^(i)(0)=0,0≤i≤n-2,u^(n-2)(1)-βu^(n-2)(ξ)=0,where 0〈t〈1,n-1〈α≤n,n≥2,ξ Е(0,1),βξ^a-n〈1. We first transform it into another equivalent boundary value problem. Then, we derive the Green's function for the equivalent boundary value problem and show that it satisfies certain properties. At last, by using some fixed-point theorems, we obtain the existence of positive solution for this problem. Example is given to illustrate the effectiveness of our result.
基金Project supported by Foundation of Major Project of ScienceTechnology of Chinese Education Ministy,NSF of Education Committee of Jiangsu Province
文摘In this paper, we consider existence of single or multiple positive solutions of three-point boundary value problems involving one-dimensional p-Laplacian. We then study existence of solutions when the problems are in resonance cases. The proposed approach is based on the Krasnoselskii's fixed point theorem and the coincidence degree.
文摘In this paper, we study the existence of positive solutions for a class of third-order three-point boundary value problem. By employing the fixed point theorem on cone, some new criteria to ensure the three-point boundary value problem has at least three positive solutions are obtained. An example illustrating our main result is given. Moreover, some previous results will be improved significantly in our paper.
基金Supported by the HEBNSF of China(A2012506010)Supported by the YSF of Heibei Province(A2014506016)
文摘In this paper, we consider the three-point boundary value problem (φp(uˊˊ(t)))ˊ +a(t)f(t, u(t), uˊ(t), uˊˊ(t)) = 0, t ∈ [0, 1] subject to the boundary conditions u(0) =βuˊ(0), uˊ(1) = αuˊ(η), uˊˊ(0) = 0, where φp(s) = |s|p?2s with p 〉 1, 0 〈 α, η 〈 1 and 0 ≤ β 〈 1. Applying a fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions to the above boundary value problem.
文摘The existence of positive solutions is established for a nonlinear second-order three-point boundary value problem. The result improves and extends the main result in Electron J. Differential Equations, 34(1999), 1-8.
文摘Married female adolescents are the most vulnerable people that culturally marry with their parents’ permission in Iran. This study aimed to investigate the effectiveness of stress inoculation training (SIT) on cognitive emotional regulation (CER) in these women. The method of this research was semi-experiment with pretest and posttest. The statistical society was the married adolescent female students from Qom high schools (80 people). First, they were assessed by cognitive emotional regulation questionnaire to find the subjects under the CER cut of point (55 people). Then 30 participants were randomly selected and were equally divided into experimental and control groups. The entry criteria for samples were female married students between 17 and 19 from low socioeconomic income. The experimental group received 8 sessions of SIT training while there was no intervention for control group. Results from MANCOVA analysis showed that there were significant differences between groups on cognitive emotional regulation in post-test. The data of pretest were the covariate factor. Finding suggests SIT is effective for cognitive emotional regulation in vulnerable married female adolescents. In addition, this training method elevates positive emotional strategies, which correlate with planning, focusing and organizing the emotions. In contrast, except self and the others blaming, negative emotional strategies differed slightly.
基金Supported by the National Natural Science Foundation of China(11261053) Supported by the Natural Science Foundation of Gansu Province of China(1308RJZA125)
文摘In this paper, the second-order three-point boundary value problem u(t) + λa(t)f(t, u(t)) = 0, 0 < t < 1,u(t) = u(1- t), u(0)- u(1) = u(12)is studied, where λ is a positive parameter, under various assumption on a and f, we establish intervals of the parameter λ, which yield the existence of positive solution, our proof based on Krasnosel'skii fixed-point theorem in cone.{u"(t)+λa(t)f(t,u(t))=0,0<t<1,u(t)=u(1-t),u′(0)-u′(1)=u(1/2)is studied,where A is a positive parameter,under various assumption on a and f,we establish intervals of the parameter A,which yield the existence of positive solution,our proof based on Krasnosel'skii fixed-point theorem in cone.
基金Supported by the National Natural Sciences Foundation of China( 1 0 0 61 0 0 4 ) and the Natural SciencesFoundation of Yunnan Province
文摘By using the Krasnoselskii's fixed point theorem for cones,conditions for the existence of positive solutions to the three-point boundary value problem for second order differential equation with an advanced argumentu″(t)+λa(t)f(u(h(t)))=0, t∈(0,1), u(0)=0, αu(η)=u(1),where 0<η<1,0<α<1η and t≤h(t)≤1 are obtained.
文摘This paper is devoted to the study of the existence and uniqueness of the positive solution for a type of the nonlinear third-order three-point boundary value problem. Our results are based on an iterative method and the Leray-Schauder fixed point theorem.
基金the Natural Science Foundation of Zhejiang Province of China (Y605144)the XNF of Zhejiang University of Media and Communications (XN08001)
文摘In this paper, the existence of monotone positive solution for the following secondorder three-point boundary value problem is studied:x″(t)+f(t,x(t))=0,0〈t〈1,x′(0)=0,x(1)+δx′(η)=0,where η ∈ (0, 1), δ∈ [0, ∞), f ∈ C([0, 1] × [0, ∞), [0, ∞)). Under certain growth conditions on the nonlinear term f and by using a fixed point theorem of cone expansion and compression of functional type due to Avery, Anderson and Krueger, sufficient conditions for the existence of monotone positive solution are obtained and the bounds of solution are given. At last, an example is given to illustrate the result of the paper.
文摘Using the method of lower and upper solutions, we study the following singular nonlinear three-point boundary value problems: , where K ∈ C[0,1] ,0 α η < 1 and λ is a positive parameter and present the existence, uniqueness, and the dependency on parameters of the positive solutions under various assumptions. Our result improves those in the previous literatures.
文摘In this paper, we investigate the existence of positive solutions for a singular third-order three-point boundary value problem with a parameter. By using fixed point index theory, some existence, multiplicity and nonexistence results for positive solutions are derived in terms of different values of λ.