The Leray-Schauder topological degree theory is established in the probabilistic linearnormed spaces.Based.on this theory,some fixed point theorems for mappings in theprobabilistic linear normed spaces are shown.
The main purpose of this paper is devoted to generalizing the results of Browder[1,2]This paper consists of four parts. In the first part, we introduce the concepts of multivalued (S) and (S), type mappings and the co...The main purpose of this paper is devoted to generalizing the results of Browder[1,2]This paper consists of four parts. In the first part, we introduce the concepts of multivalued (S) and (S), type mappings and the concepts of the limits of multivalued (S) and (S) + type mappings. These kinds of mappings contain many monotone type mappings, such as maximal monotone mapping, bounded pseudo-monotone mapping and bounded generalized pseudo-monotone mapping, as its special cases. In the second part we define the pseudo-degree for (S) type mapping and the degree for (S)+ type mapping. These two kinds of degrees are all the generalizations of the degree defined by Browder[1,2] As applications, we utilize the degree theory presented in part 2 to study the existence of solutions for the multivalued operator equations (see part 3) and to obtain some new fixed point theorems in part 4.展开更多
In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain.Under some smallness and structural assumptions imposed on the time-p...In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain.Under some smallness and structural assumptions imposed on the time-periodic force,we establish the existence of the time-periodic solutions to the system by using a regularized approximation scheme and the topological degree theory.We also prove a uniqueness result via energy estimates.展开更多
Using the theory of coincidence degree, a class of higher order multi-point boundary value problem for ordinary differential equations are studied. Under the boundary conditions satisfying the resonance case, some new...Using the theory of coincidence degree, a class of higher order multi-point boundary value problem for ordinary differential equations are studied. Under the boundary conditions satisfying the resonance case, some new existence results are obtained by supposing some conditions to the nonlinear term and applying a priori estimates.展开更多
A kind of third order multi-point boundary value problems, x'''( ι) = f( t, x ( t ), x" ( t ), x''' ( t ) ) + m 2 e(t),t∈(0, 1),x(0)=ax(ξ),x'(0)-0,x(l)= ^m2∑j=1 βjx(ηj), fεC[0,...A kind of third order multi-point boundary value problems, x'''( ι) = f( t, x ( t ), x" ( t ), x''' ( t ) ) + m 2 e(t),t∈(0, 1),x(0)=ax(ξ),x'(0)-0,x(l)= ^m2∑j=1 βjx(ηj), fεC[0, 1]×R^3, e(t)∈L^1[0, 1],a≥0, is considered, all theβj's have not the same sign, 0〈ξ〈 l, 0〈η1〈 η2〈… 〈ηm.2〈 1. By using the coincidence degree theory, some existence theorems for the problems at resonance are obtained.展开更多
The existence of solutions at resonance is obtained by using the an example to demonstrate our result. noncontinuous. for the 2n-order m-point boundary value problem coincidence degree theory of Mawhin. We give The ...The existence of solutions at resonance is obtained by using the an example to demonstrate our result. noncontinuous. for the 2n-order m-point boundary value problem coincidence degree theory of Mawhin. We give The interest is that the nonlinear term may be展开更多
In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays (CNNVDs) is considered. By using the methods of the topological degree theory and generaliz...In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays (CNNVDs) is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improved and extended in this letter and one example is given to illustrate the effectiveness of the new results.展开更多
In this study, the impulsive predator-prey dynamic systems on time scales calculus are studied. When the system has periodic solution is investigated, and three different conditions have been found, which are necessar...In this study, the impulsive predator-prey dynamic systems on time scales calculus are studied. When the system has periodic solution is investigated, and three different conditions have been found, which are necessary for the periodic solution of the predator-prey dynamic systems with Beddington-DeAngelis type functional response. For this study the main tools are time scales calculus and coincidence degree theory. Also the findings are beneficial for continuous case, discrete case and the unification of both these cases. Additionally, unification of continuous and discrete case is a good example for the modeling of the life cycle of insects.展开更多
This paper is concerned with two aspects of the fractional Navier-Stokes equation. First, we establish the local L^(2)theory of the hypo-dissipative Navier-Stokes system. More precisely, the existence of local-in-time...This paper is concerned with two aspects of the fractional Navier-Stokes equation. First, we establish the local L^(2)theory of the hypo-dissipative Navier-Stokes system. More precisely, the existence of local-in-time as well as global-in-time local energy weak solutions to the hypo-dissipative Navier-Stokes system is proved.In particular, in order to construct a pressure with an explicit representation, some technical innovations are required due to the lack of known results on the local regularity of the non-local Stokes operator. Secondly, as an important application to the local L^(2)theory, we give a second construction of large self-similar solutions of the hypo-dissipative Navier-Stokes system along with the Leray-Schauder degree theory.展开更多
In this paper,by applying Comparison Theorem of differential equation,Continuation Theorem of coincidence degree theory,Barbalat Lemma and Lyapunov Function,a diffusion system with distributive time delay and ratio-de...In this paper,by applying Comparison Theorem of differential equation,Continuation Theorem of coincidence degree theory,Barbalat Lemma and Lyapunov Function,a diffusion system with distributive time delay and ratio-dependence functional response is studied.It is proved that the system is uniformly persistent under appropriate conditions.Further,if the system is a periodic one,it can have a strictly positive periodic solution which is globally asymptotically stable under appropriations.Some new results are obtained.展开更多
A kind of multiple attribute group decision making (MAGDM) problem is discussed from the perspective of statistic decision-making. Firstly, on the basis of the stability theory, a new idea is proposed to solve this ...A kind of multiple attribute group decision making (MAGDM) problem is discussed from the perspective of statistic decision-making. Firstly, on the basis of the stability theory, a new idea is proposed to solve this kind of problem. Secondly, a con- crete method corresponding to this kind of problem is proposed. The main tool of our research is the technique o~ the jackknife method. The main advantage of the new method is that it can identify and determine the reliability degree of the existed decision making information. Finally, a traffic engineering example is given to show the effectiveness of the new method.展开更多
LetΩbe a bounded smooth domain in RN(N≥3).Assuming that 0<s<1,1<p,q≤N+2s/N-2s with(p,q)≠(N+2s/N-2s,N+2s/N-2s),and a,b>0 are constants,we consider the existence results for positive solutions of a class...LetΩbe a bounded smooth domain in RN(N≥3).Assuming that 0<s<1,1<p,q≤N+2s/N-2s with(p,q)≠(N+2s/N-2s,N+2s/N-2s),and a,b>0 are constants,we consider the existence results for positive solutions of a class of fractional elliptic system below,{(a+b[u]^(2)_(s))(-Δ)^(s)u=vp+h_(1)(x,u,v,▽u,▽v),x∈Ω,(-Δ)^(s)v=u^(q)+h_(2)(x,u,▽,▽u,▽v),x∈Q,u,v>0,x∈Ω,u=v=0,x∈RN\Ω.Under some assumptions of hi(x,u,v,▽u,▽v)(i=1,2),we get a priori bounds of the positive solutions to the problem(1.1)by the blow-up methods and rescaling argument.Based on these estimates and degree theory,we establish the existence of positive solutions to problem(1.1).展开更多
This paper is devoted to the applications of classical topological degrees to nonlinear problems involving various classes of operators acting between ordered Banach spaces. In this framework, the Leray-Schauder, Brow...This paper is devoted to the applications of classical topological degrees to nonlinear problems involving various classes of operators acting between ordered Banach spaces. In this framework, the Leray-Schauder, Browder-Petryshyn, and Amann-Weiss degree theories are considered, and several existence results are obtained. The non-Archimedean case is also discussed.展开更多
In this paper,by a coincidence degree theory,the existence of periodic solutions to a Linard equation with multiple delays is established,which substantially extends some results in the previous literatures.
The elliptical cross-section spiral equal-channel extrusion (ECSEE) process is simulated by using Deform-3D finite element software. The ratio m of major-axis to minor-axis length for ellipse-cross-section, the tors...The elliptical cross-section spiral equal-channel extrusion (ECSEE) process is simulated by using Deform-3D finite element software. The ratio m of major-axis to minor-axis length for ellipse-cross-section, the torsion angle u, the round-ellipse cross-section transitional channel L1, the elliptical rotation cross-section transitional channel L2 and the ellipse-round cross-section transitional channel L3 are destined for the extrusion process parameters. The average effective strain eave on cross-section of blank, the deformation uniformity coefficient a and the value of maximum damage dmax are chosen to be the optimize indexes, and the virtual orthogonal experiment of L16 (45) is designed. The correlation degree of the process factors affecting eave, a and dmax is analyzed by the numerical simulation results using the weights and grey association model. The process parameters are optimized by introducing the grey situation decision theory and the ECSEE optimal combination of process parameters is obtained: u of 120 , m of 1.55, L1 of 7 mm, L2 of 10 mm, and L3 of 10 mm. Simulation and experimental results show that the material can be refined with the optimized structural parameters of die. Therefore, the optimization results are satisfactory.展开更多
This paper concerns the controllability of autonomous and nonautonomous nonlinear discrete systems,in which linear parts might admit certain degeneracy.By introducing Fredholm operators and coincidence degree theory,s...This paper concerns the controllability of autonomous and nonautonomous nonlinear discrete systems,in which linear parts might admit certain degeneracy.By introducing Fredholm operators and coincidence degree theory,sufficient conditions for nonlinear discrete systems to be controllable are presented.In addition,applications are given to illustrate main results.展开更多
The main propose of this paper is devoted to study the solvability of the generalized order tensor complementarity problem.We define two problems:the generalized order tensor complementarity problem and the vertical t...The main propose of this paper is devoted to study the solvability of the generalized order tensor complementarity problem.We define two problems:the generalized order tensor complementarity problem and the vertical tensor comple-mentarity problem and show that the former is equivalent to the latter.Using the degree theory,we present a comprehensive analysis of existence,uniqueness and stability of the solution set of a given generalized order tensor complementarity problem.展开更多
In this paper, by the theory of Fourier series, Bernoulli number theory and continu-ation theorem of coincidence degree theory, we study a kind of higher order functional differential equation with two deviating argum...In this paper, by the theory of Fourier series, Bernoulli number theory and continu-ation theorem of coincidence degree theory, we study a kind of higher order functional differential equation with two deviating arguments. Some new results on the existence of periodic solutions are obtained.展开更多
In this paper, we are concerned with the existence of solution to a boundary value problem of nonlinear fractional differential equation at resonance. By means of the coincidence degree theory, the existence of soluti...In this paper, we are concerned with the existence of solution to a boundary value problem of nonlinear fractional differential equation at resonance. By means of the coincidence degree theory, the existence of solution is obtained.展开更多
基金The projects supported by National Natural Science Foundation of China
文摘The Leray-Schauder topological degree theory is established in the probabilistic linearnormed spaces.Based.on this theory,some fixed point theorems for mappings in theprobabilistic linear normed spaces are shown.
文摘The main purpose of this paper is devoted to generalizing the results of Browder[1,2]This paper consists of four parts. In the first part, we introduce the concepts of multivalued (S) and (S), type mappings and the concepts of the limits of multivalued (S) and (S) + type mappings. These kinds of mappings contain many monotone type mappings, such as maximal monotone mapping, bounded pseudo-monotone mapping and bounded generalized pseudo-monotone mapping, as its special cases. In the second part we define the pseudo-degree for (S) type mapping and the degree for (S)+ type mapping. These two kinds of degrees are all the generalizations of the degree defined by Browder[1,2] As applications, we utilize the degree theory presented in part 2 to study the existence of solutions for the multivalued operator equations (see part 3) and to obtain some new fixed point theorems in part 4.
基金partially supported by the Science and Technology Research Program of Chongqing Municipal Education Commission(KJQN202100523,KJQN202000536)the National Natural Science Foundation of China(12001074)+3 种基金the Natural Science Foundation of Chongqing(cstc2020jcyj-msxmX0606)supported by the National Natural Science Foundation of Chongqing(CSTB2023NSCQ-MSX0278)the Science and Technology Research Program of Chongqing Municipal Education Commission(KJZD-K202100503)the Research Project of Chongqing Education Commission(CXQT21014)。
文摘In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain.Under some smallness and structural assumptions imposed on the time-periodic force,we establish the existence of the time-periodic solutions to the system by using a regularized approximation scheme and the topological degree theory.We also prove a uniqueness result via energy estimates.
基金Project supported by the National Natural Science Foundation of China (No.10371006)
文摘Using the theory of coincidence degree, a class of higher order multi-point boundary value problem for ordinary differential equations are studied. Under the boundary conditions satisfying the resonance case, some new existence results are obtained by supposing some conditions to the nonlinear term and applying a priori estimates.
文摘A kind of third order multi-point boundary value problems, x'''( ι) = f( t, x ( t ), x" ( t ), x''' ( t ) ) + m 2 e(t),t∈(0, 1),x(0)=ax(ξ),x'(0)-0,x(l)= ^m2∑j=1 βjx(ηj), fεC[0, 1]×R^3, e(t)∈L^1[0, 1],a≥0, is considered, all theβj's have not the same sign, 0〈ξ〈 l, 0〈η1〈 η2〈… 〈ηm.2〈 1. By using the coincidence degree theory, some existence theorems for the problems at resonance are obtained.
基金the Natural Science Foundation of Hebei Province of China(No.A2006000298)the Doctoral Foundation of Hebei Province of China(No.B2004204)
文摘The existence of solutions at resonance is obtained by using the an example to demonstrate our result. noncontinuous. for the 2n-order m-point boundary value problem coincidence degree theory of Mawhin. We give The interest is that the nonlinear term may be
文摘In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays (CNNVDs) is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improved and extended in this letter and one example is given to illustrate the effectiveness of the new results.
文摘In this study, the impulsive predator-prey dynamic systems on time scales calculus are studied. When the system has periodic solution is investigated, and three different conditions have been found, which are necessary for the periodic solution of the predator-prey dynamic systems with Beddington-DeAngelis type functional response. For this study the main tools are time scales calculus and coincidence degree theory. Also the findings are beneficial for continuous case, discrete case and the unification of both these cases. Additionally, unification of continuous and discrete case is a good example for the modeling of the life cycle of insects.
基金supported by National Natural Science Foundation of China(Grant Nos.11871087 and 11971148)。
文摘This paper is concerned with two aspects of the fractional Navier-Stokes equation. First, we establish the local L^(2)theory of the hypo-dissipative Navier-Stokes system. More precisely, the existence of local-in-time as well as global-in-time local energy weak solutions to the hypo-dissipative Navier-Stokes system is proved.In particular, in order to construct a pressure with an explicit representation, some technical innovations are required due to the lack of known results on the local regularity of the non-local Stokes operator. Secondly, as an important application to the local L^(2)theory, we give a second construction of large self-similar solutions of the hypo-dissipative Navier-Stokes system along with the Leray-Schauder degree theory.
文摘In this paper,by applying Comparison Theorem of differential equation,Continuation Theorem of coincidence degree theory,Barbalat Lemma and Lyapunov Function,a diffusion system with distributive time delay and ratio-dependence functional response is studied.It is proved that the system is uniformly persistent under appropriate conditions.Further,if the system is a periodic one,it can have a strictly positive periodic solution which is globally asymptotically stable under appropriations.Some new results are obtained.
基金supported by the National Key Basic Research Program of China(973 Program)(2012CB725402)the National High-Tech R&D Program of China(863 Program)(SS2014AA110303)the Science Foundation for Post-doctoral Scientists of Jiangsu Province(1301011A)
文摘A kind of multiple attribute group decision making (MAGDM) problem is discussed from the perspective of statistic decision-making. Firstly, on the basis of the stability theory, a new idea is proposed to solve this kind of problem. Secondly, a con- crete method corresponding to this kind of problem is proposed. The main tool of our research is the technique o~ the jackknife method. The main advantage of the new method is that it can identify and determine the reliability degree of the existed decision making information. Finally, a traffic engineering example is given to show the effectiveness of the new method.
基金supported by National Natural Science Foundation of China (No.11761030)Hubei Provincial Natural Science Foundation of China (No.2022CFC016)Cultivation Project for High-Level Scientific Research Achievements of Hubei Minzu University (No.PY20002)。
文摘LetΩbe a bounded smooth domain in RN(N≥3).Assuming that 0<s<1,1<p,q≤N+2s/N-2s with(p,q)≠(N+2s/N-2s,N+2s/N-2s),and a,b>0 are constants,we consider the existence results for positive solutions of a class of fractional elliptic system below,{(a+b[u]^(2)_(s))(-Δ)^(s)u=vp+h_(1)(x,u,v,▽u,▽v),x∈Ω,(-Δ)^(s)v=u^(q)+h_(2)(x,u,▽,▽u,▽v),x∈Q,u,v>0,x∈Ω,u=v=0,x∈RN\Ω.Under some assumptions of hi(x,u,v,▽u,▽v)(i=1,2),we get a priori bounds of the positive solutions to the problem(1.1)by the blow-up methods and rescaling argument.Based on these estimates and degree theory,we establish the existence of positive solutions to problem(1.1).
文摘This paper is devoted to the applications of classical topological degrees to nonlinear problems involving various classes of operators acting between ordered Banach spaces. In this framework, the Leray-Schauder, Browder-Petryshyn, and Amann-Weiss degree theories are considered, and several existence results are obtained. The non-Archimedean case is also discussed.
文摘In this paper,by a coincidence degree theory,the existence of periodic solutions to a Linard equation with multiple delays is established,which substantially extends some results in the previous literatures.
基金co-supported by National Natural Science Foundation of China (No. 51275414)Aeronautical Science Foundation of China (No. 2011ZE53059)+1 种基金National Defense Basic Research Program (No. 51318040105)Graduate Starting Seed Fund of Northwestern Polytechnical University(No. Z2011006)
文摘The elliptical cross-section spiral equal-channel extrusion (ECSEE) process is simulated by using Deform-3D finite element software. The ratio m of major-axis to minor-axis length for ellipse-cross-section, the torsion angle u, the round-ellipse cross-section transitional channel L1, the elliptical rotation cross-section transitional channel L2 and the ellipse-round cross-section transitional channel L3 are destined for the extrusion process parameters. The average effective strain eave on cross-section of blank, the deformation uniformity coefficient a and the value of maximum damage dmax are chosen to be the optimize indexes, and the virtual orthogonal experiment of L16 (45) is designed. The correlation degree of the process factors affecting eave, a and dmax is analyzed by the numerical simulation results using the weights and grey association model. The process parameters are optimized by introducing the grey situation decision theory and the ECSEE optimal combination of process parameters is obtained: u of 120 , m of 1.55, L1 of 7 mm, L2 of 10 mm, and L3 of 10 mm. Simulation and experimental results show that the material can be refined with the optimized structural parameters of die. Therefore, the optimization results are satisfactory.
基金supported by National Natural Science Foundation of China (grant No.41874132)supported by National Natural Science Foundation of China (grant No.11201173)+3 种基金National Natural Science Foundation of China (grant No.11171132,grant No.11571065)Science and Technology Developing Plan of Jilin Province (grant No.20180101220JC)supported by National Basic Research Program of China (grant No.2013CB834100)Jilin DRC (grant No.2017C028-1)。
文摘This paper concerns the controllability of autonomous and nonautonomous nonlinear discrete systems,in which linear parts might admit certain degeneracy.By introducing Fredholm operators and coincidence degree theory,sufficient conditions for nonlinear discrete systems to be controllable are presented.In addition,applications are given to illustrate main results.
基金The first author is supported by the Fundamental Research Funds for the Central Universities under grant No.JBK1801058Partial work is fin-ished during the author’s visiting at Shanghai Key Laboratory of Contemporary Ap-plied Mathematics+2 种基金The second author is supported by the Hong Kong Research Grant Council(Grant Nos.PolyU 501913,15302114,15300715 and 15301716)The third author is supported by the National Natural Science Foundation of China under grant No.11771099Innovation Program of Shanghai Municipal Education Commission.We would like to thank the editor and two anonymous reviewers for very helpful com-ments.
文摘The main propose of this paper is devoted to study the solvability of the generalized order tensor complementarity problem.We define two problems:the generalized order tensor complementarity problem and the vertical tensor comple-mentarity problem and show that the former is equivalent to the latter.Using the degree theory,we present a comprehensive analysis of existence,uniqueness and stability of the solution set of a given generalized order tensor complementarity problem.
基金Natural Science Foundation of Anhui Province (050460103)the Key Natural Science Foundation by the Bureau of Education of Anhui Province(KJ2008A05ZC).
文摘In this paper, by the theory of Fourier series, Bernoulli number theory and continu-ation theorem of coincidence degree theory, we study a kind of higher order functional differential equation with two deviating arguments. Some new results on the existence of periodic solutions are obtained.
基金supported by the NSF of Shandong (ZR2010AM035, ZR2009GZ001)the NNSF of China (60874032, 11026176)
文摘In this paper, we are concerned with the existence of solution to a boundary value problem of nonlinear fractional differential equation at resonance. By means of the coincidence degree theory, the existence of solution is obtained.