In this paper, we prove some intersection theorems concerning noncompact sets with H-convex sections which generalize the corresponding results of Ma, Fan, Tarafdar, Lassonde and Shin-Tan to H-spaces without the linea...In this paper, we prove some intersection theorems concerning noncompact sets with H-convex sections which generalize the corresponding results of Ma, Fan, Tarafdar, Lassonde and Shin-Tan to H-spaces without the linear structure and to noncompact setting. An application to von Neumann type minimax theorems is given.展开更多
The existence of solutions of a Sturm Liouville boundary value problem(BVP) for u″+g(u)=p(t,u,u′)(0≤t≤1) is studied by using a continuation theorem based on the topological degree theory. Under the condition that...The existence of solutions of a Sturm Liouville boundary value problem(BVP) for u″+g(u)=p(t,u,u′)(0≤t≤1) is studied by using a continuation theorem based on the topological degree theory. Under the condition that g grows superlinearly and p grows with respect to u and u′ linearly at most, the boundary value problem has an infinitude of solutions.展开更多
By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(...By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(t)N′(t-τ(t))].展开更多
By using the continuation theorem of coincidence theory, the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional responsex [FK(W1*3/4。*2/3]...By using the continuation theorem of coincidence theory, the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional responsex [FK(W1*3/4。*2/3]′ 1 (t)=x 1(t)a 1(t)-b 1(t)x 1(t)-c 1(t)y(t)1+m(t)x 1(t)+D 1(t)[x 2(t)-x 1(t)], x [FK(W1*3/4。*2/3]′ 2 (t)=x 2(t)a 2(t)-b 2(t)x 2(t)-c 2(t)∫ 0 -τ k(s)x 2(t+s) d s+D 2(t)[x 1(t)-x 2(t)], y′(t)=y(t)a 3(t)-b 3(t)y(t)-c 3(t)x 1(t)1+m(t)x 1(t)is established, where a i(t),b i(t),c i(t)(i=1,2,3),m(t) and D i(t)(i=1,2) are all positive periodic continuous functions with period w >0, τ is a nonnegative constant and k(s) is a continuous nonnegative function on [- τ ,0].展开更多
In this paper, a three species diffusive predator-prey model with functional response is studied, where all parameters are time dependent. By using the continuation theorem of coincidence degree theory, the existence ...In this paper, a three species diffusive predator-prey model with functional response is studied, where all parameters are time dependent. By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for this system is established.展开更多
Based on Mansevich-Mawhin continuation theorem and some analysis skill,some sufficient conditions for the existence of periodic solutions for mixed type p-Laplacian equation with deviating arguments are established,...Based on Mansevich-Mawhin continuation theorem and some analysis skill,some sufficient conditions for the existence of periodic solutions for mixed type p-Laplacian equation with deviating arguments are established,which are complement of previously known results.展开更多
By means of an extension of Mawhin's continuation theorem and some analysis methods, the existence of a set with 2kT-periodic solutions for a class of second order neutral functional differential systems is studied, ...By means of an extension of Mawhin's continuation theorem and some analysis methods, the existence of a set with 2kT-periodic solutions for a class of second order neutral functional differential systems is studied, and then the homoclinic solutions are obtained as the limit points of a certain subsequence of the above set.展开更多
By means of Mawhin's continuation theorem,we study a kind of lie'nard functional differential equations:x"(t)+f(x(t))x'(t)+g(t,x(t-τ(t))) = e(t).Some new results on the existence and uniqueness of pe...By means of Mawhin's continuation theorem,we study a kind of lie'nard functional differential equations:x"(t)+f(x(t))x'(t)+g(t,x(t-τ(t))) = e(t).Some new results on the existence and uniqueness of periodic solutions are obtained.展开更多
This paper is concerned with the existence of solutions for the following multipoint boundary value problem at resonance{(Φp (x'))' + f(t,x)=0,0 < t < 1,x' (0)=x'(ξ) x(1)=m-3 ∑i=1 βi x(η i),...This paper is concerned with the existence of solutions for the following multipoint boundary value problem at resonance{(Φp (x'))' + f(t,x)=0,0 < t < 1,x' (0)=x'(ξ) x(1)=m-3 ∑i=1 βi x(η i),where βi∈ R,m-3 ∑i=1 β i=1,0 < η 1 < η 2 < ··· < ηm-3 < 1,m-3 ∑i=1 βiηi=1,0 < ξ < 1.An existence theorem is obtained by using the extension of Mawhin's continuation theorem.Since almost all the multi-point boundary value problem at resonance in previous papers are for the linear operator without p-Laplacian by the use of Mawhin's continuation theorem,our method is new.展开更多
The sufficient condition for the existence of2 π- periodic solutions of the following third- order functional differential equations with variable coefficients a(t) x (t) +bx″2 k- 1(t) +cx′2 k- 1(t) + 2 k- 1 i=1...The sufficient condition for the existence of2 π- periodic solutions of the following third- order functional differential equations with variable coefficients a(t) x (t) +bx″2 k- 1(t) +cx′2 k- 1(t) + 2 k- 1 i=1 cixi(t) +g(x(t-τ) ) =p(t) =p(t+2π) is obtained.The approach is based on the abstract continuation theorem from Mawhin and the a- priori estimate of periodic solutions展开更多
The existence of solutions for second order three-point boundary value problems with nonlinear growth at resonance is studied by using Mawhin continuation theorem. The result shows that theorem 1 and 2 at least have o...The existence of solutions for second order three-point boundary value problems with nonlinear growth at resonance is studied by using Mawhin continuation theorem. The result shows that theorem 1 and 2 at least have one solution in c1[0,1]展开更多
By means of the continuation theorem of the coincidence degree theory,the existence of two periodic solutions of a delayed single species model with feedback regulation and harvest term is obtained.
This paper is concerned with the non-Newtonian filtration equations with non- linear sources and a time-varying delay. By an extension of Mawhin's continuation theorem and some analysis methods, several sufficient co...This paper is concerned with the non-Newtonian filtration equations with non- linear sources and a time-varying delay. By an extension of Mawhin's continuation theorem and some analysis methods, several sufficient conditions ensuring the existence of solitary wave and periodic wave solutions are obtained. Some corresponding results in the literature are improved and extended. An example is given to illustrate the effectiveness of our results.展开更多
A set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions for delayed generalized predator-prey dispersion systemwhere ai(t),bi(t) and Di(t)(i = 1, 2) axe positive c...A set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions for delayed generalized predator-prey dispersion systemwhere ai(t),bi(t) and Di(t)(i = 1, 2) axe positive continuous T-periodic functions, gi(t,xi) (i = 1,2) and h(t,y) are continuous and T-periodic with respect to t and h(t,y) > 0 for y>0,t, y∈R,pi(x)(i=1,2) are continuous and monotonously increasing functions, and Pi(xi)>0 for xi>0.展开更多
Homoclinic solutions were introduced for a prescribed mean curvature Lienard p-Laplacian equation with a deviating argument.It was divided into three parts to discuss the existence of homoclinic solutions.By using an ...Homoclinic solutions were introduced for a prescribed mean curvature Lienard p-Laplacian equation with a deviating argument.It was divided into three parts to discuss the existence of homoclinic solutions.By using an extension of Mawhin's continuation theorem,the existence of a set with 2kT-periodic for a prescribed mean curvature Lienard p-Laplacian equation with a deviating argument was studied.According to a limit on a certain subsequence of 2kT-periodic set,homoclinic solutions were obtained.A numerical example demonstrates the validity of the main results.展开更多
Sufficient conditions were given to assert that between any two Banach spaces over K, Fredholm mappings share at least one .value in a specific open ball. The proof of the result is constructive and based upon continu...Sufficient conditions were given to assert that between any two Banach spaces over K, Fredholm mappings share at least one .value in a specific open ball. The proof of the result is constructive and based upon continuation methods.展开更多
In this paper,we discuss the anti-periodic boundary value problem for a class of first order differential equations.By using homotopy method,we obtain the conditions for the existence of anti-periodic solution for the...In this paper,we discuss the anti-periodic boundary value problem for a class of first order differential equations.By using homotopy method,we obtain the conditions for the existence of anti-periodic solution for the equation under consideration.This result can be extended to higher order differential equations.展开更多
In this paper, the theorem of structure continual variation of truss structure in the analysis of structure reliability is derived, and it is used to generate limit state function automatically. We can avoid repeated ...In this paper, the theorem of structure continual variation of truss structure in the analysis of structure reliability is derived, and it is used to generate limit state function automatically. We can avoid repeated assembly of global stiffness matrix and repeated inverse operations of the matrix caused by constant changes of structure topology. A new criterion of degenerate of the structure into mechanism is introduced. The calculation examples are satisfactory.展开更多
In this paper, a biological model for two predators and one prey with impulses and periodic delays is considered. By assuming that one predator consumes prey according to Holling II functional response while the other...In this paper, a biological model for two predators and one prey with impulses and periodic delays is considered. By assuming that one predator consumes prey according to Holling II functional response while the other predators consume prey according to the Beddington-DeAngelis functional response, based on the coincidence degree theory, the existence of positive periodic solutions of nonautonomous predator-prey system with impulses and periodic delays is obtained under suitable conditions.展开更多
<div style="text-align:justify;"> <span style="font-family:Verdana;">We first recall the sufficient conditions for the existence of a periodic output of a modified Elman neural network ...<div style="text-align:justify;"> <span style="font-family:Verdana;">We first recall the sufficient conditions for the existence of a periodic output of a modified Elman neural network with a periodic input found by using Mawhin’s continuation theorem of coincidence degree theory. Using this result, we obtain sufficient conditions for the existence of a periodic output for an output hidden feedback Elman neural network with a periodic input. Examples illustrating these sufficient conditions are given.</span> </div>展开更多
文摘In this paper, we prove some intersection theorems concerning noncompact sets with H-convex sections which generalize the corresponding results of Ma, Fan, Tarafdar, Lassonde and Shin-Tan to H-spaces without the linear structure and to noncompact setting. An application to von Neumann type minimax theorems is given.
文摘The existence of solutions of a Sturm Liouville boundary value problem(BVP) for u″+g(u)=p(t,u,u′)(0≤t≤1) is studied by using a continuation theorem based on the topological degree theory. Under the condition that g grows superlinearly and p grows with respect to u and u′ linearly at most, the boundary value problem has an infinitude of solutions.
基金National Natural Science Foundation of China( 198710 0 5 )
文摘By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(t)N′(t-τ(t))].
文摘By using the continuation theorem of coincidence theory, the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional responsex [FK(W1*3/4。*2/3]′ 1 (t)=x 1(t)a 1(t)-b 1(t)x 1(t)-c 1(t)y(t)1+m(t)x 1(t)+D 1(t)[x 2(t)-x 1(t)], x [FK(W1*3/4。*2/3]′ 2 (t)=x 2(t)a 2(t)-b 2(t)x 2(t)-c 2(t)∫ 0 -τ k(s)x 2(t+s) d s+D 2(t)[x 1(t)-x 2(t)], y′(t)=y(t)a 3(t)-b 3(t)y(t)-c 3(t)x 1(t)1+m(t)x 1(t)is established, where a i(t),b i(t),c i(t)(i=1,2,3),m(t) and D i(t)(i=1,2) are all positive periodic continuous functions with period w >0, τ is a nonnegative constant and k(s) is a continuous nonnegative function on [- τ ,0].
文摘In this paper, a three species diffusive predator-prey model with functional response is studied, where all parameters are time dependent. By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for this system is established.
基金Foundation item: Supported by the Foundation of Education Department of Jiangxi Province(G J J11234) Supported by the Natural Science Foundation of Jiangxi Province(2009GQS0023) Supported by the Natural Science Foundation of Shangrao Normal University(1001)
文摘Based on Mansevich-Mawhin continuation theorem and some analysis skill,some sufficient conditions for the existence of periodic solutions for mixed type p-Laplacian equation with deviating arguments are established,which are complement of previously known results.
基金sponsored by the National Natural Science Foundation of China(11271197)the Science and Technology Foundation in Ministry of Education of China(207047)the Science Foundation of NUIST of China(20090202 and 2012r101)
文摘By means of an extension of Mawhin's continuation theorem and some analysis methods, the existence of a set with 2kT-periodic solutions for a class of second order neutral functional differential systems is studied, and then the homoclinic solutions are obtained as the limit points of a certain subsequence of the above set.
基金Foundation item: Supported by the Anhui Natural Science Foundation(050460103) Supported by the NSF of Anhui Educational Bureau(KJ2008B247) Supported by the RSPYT of Anhui Educational Bu- reau(2008jq1111)
文摘By means of Mawhin's continuation theorem,we study a kind of lie'nard functional differential equations:x"(t)+f(x(t))x'(t)+g(t,x(t-τ(t))) = e(t).Some new results on the existence and uniqueness of periodic solutions are obtained.
文摘This paper is concerned with the existence of solutions for the following multipoint boundary value problem at resonance{(Φp (x'))' + f(t,x)=0,0 < t < 1,x' (0)=x'(ξ) x(1)=m-3 ∑i=1 βi x(η i),where βi∈ R,m-3 ∑i=1 β i=1,0 < η 1 < η 2 < ··· < ηm-3 < 1,m-3 ∑i=1 βiηi=1,0 < ξ < 1.An existence theorem is obtained by using the extension of Mawhin's continuation theorem.Since almost all the multi-point boundary value problem at resonance in previous papers are for the linear operator without p-Laplacian by the use of Mawhin's continuation theorem,our method is new.
基金Supported by the National Natural Science Foundation of China(1 9971 0 2 6 )
文摘The sufficient condition for the existence of2 π- periodic solutions of the following third- order functional differential equations with variable coefficients a(t) x (t) +bx″2 k- 1(t) +cx′2 k- 1(t) + 2 k- 1 i=1 cixi(t) +g(x(t-τ) ) =p(t) =p(t+2π) is obtained.The approach is based on the abstract continuation theorem from Mawhin and the a- priori estimate of periodic solutions
文摘The existence of solutions for second order three-point boundary value problems with nonlinear growth at resonance is studied by using Mawhin continuation theorem. The result shows that theorem 1 and 2 at least have one solution in c1[0,1]
基金Supported by the Science and Technical Foundation to Hubei University of Technology[2006(5)]
文摘By means of the continuation theorem of the coincidence degree theory,the existence of two periodic solutions of a delayed single species model with feedback regulation and harvest term is obtained.
基金supported by the National Natural Science Foundation of China(11471109)the Construct Program of the Key Discipline in Hunan Province and Hunan Provincial Innovation Foundation for Postgraduate(CX2017B172)
文摘This paper is concerned with the non-Newtonian filtration equations with non- linear sources and a time-varying delay. By an extension of Mawhin's continuation theorem and some analysis methods, several sufficient conditions ensuring the existence of solitary wave and periodic wave solutions are obtained. Some corresponding results in the literature are improved and extended. An example is given to illustrate the effectiveness of our results.
基金The project is supported by Youth Project Foundation of Hubei Education Department (2002B00002)the Scientific Research Foundation of Hubei Normal University(2003).
文摘A set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions for delayed generalized predator-prey dispersion systemwhere ai(t),bi(t) and Di(t)(i = 1, 2) axe positive continuous T-periodic functions, gi(t,xi) (i = 1,2) and h(t,y) are continuous and T-periodic with respect to t and h(t,y) > 0 for y>0,t, y∈R,pi(x)(i=1,2) are continuous and monotonously increasing functions, and Pi(xi)>0 for xi>0.
基金Natural Foundation of Wuyi University,China(No.XQ201305)Young-Middle-Aged Teachers Education Scientific Research Project in Fujian Province,China(No.JA15524)
文摘Homoclinic solutions were introduced for a prescribed mean curvature Lienard p-Laplacian equation with a deviating argument.It was divided into three parts to discuss the existence of homoclinic solutions.By using an extension of Mawhin's continuation theorem,the existence of a set with 2kT-periodic for a prescribed mean curvature Lienard p-Laplacian equation with a deviating argument was studied.According to a limit on a certain subsequence of 2kT-periodic set,homoclinic solutions were obtained.A numerical example demonstrates the validity of the main results.
基金Project supported by D.G.E.S. Pb 96-1338-CO 2-01 and the Junta de Andalucia
文摘Sufficient conditions were given to assert that between any two Banach spaces over K, Fredholm mappings share at least one .value in a specific open ball. The proof of the result is constructive and based upon continuation methods.
文摘In this paper,we discuss the anti-periodic boundary value problem for a class of first order differential equations.By using homotopy method,we obtain the conditions for the existence of anti-periodic solution for the equation under consideration.This result can be extended to higher order differential equations.
文摘In this paper, the theorem of structure continual variation of truss structure in the analysis of structure reliability is derived, and it is used to generate limit state function automatically. We can avoid repeated assembly of global stiffness matrix and repeated inverse operations of the matrix caused by constant changes of structure topology. A new criterion of degenerate of the structure into mechanism is introduced. The calculation examples are satisfactory.
文摘In this paper, a biological model for two predators and one prey with impulses and periodic delays is considered. By assuming that one predator consumes prey according to Holling II functional response while the other predators consume prey according to the Beddington-DeAngelis functional response, based on the coincidence degree theory, the existence of positive periodic solutions of nonautonomous predator-prey system with impulses and periodic delays is obtained under suitable conditions.
文摘<div style="text-align:justify;"> <span style="font-family:Verdana;">We first recall the sufficient conditions for the existence of a periodic output of a modified Elman neural network with a periodic input found by using Mawhin’s continuation theorem of coincidence degree theory. Using this result, we obtain sufficient conditions for the existence of a periodic output for an output hidden feedback Elman neural network with a periodic input. Examples illustrating these sufficient conditions are given.</span> </div>