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
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, by using the fixed-point index theory, we study the existence of sign-changing solution of some three-point boundary value problems {y ''(t) + f(y) = 0, t ∈ [0, 1], y' (0) = 0, y(1) = αy(...In this paper, by using the fixed-point index theory, we study the existence of sign-changing solution of some three-point boundary value problems {y ''(t) + f(y) = 0, t ∈ [0, 1], y' (0) = 0, y(1) = αy(η), where 0 < α < 1, 0 < η < 1, f : R → R is continuous, strictly increasing and f(0) = 0.展开更多
We study the existence of solutions to the second order three-point boundary value problem：{x″（t）＋f（t,x（t）,x′（t））=0,t≠ti,△x（ti）=Ii（x（ti）,x′（ti））,i=1,2,…,k,△x′（ti）=Ji（x（ti）,x′（t））,i=1...We study the existence of solutions to the second order three-point boundary value problem：{x″（t）＋f（t,x（t）,x′（t））=0,t≠ti,△x（ti）=Ii（x（ti）,x′（ti））,i=1,2,…,k,△x′（ti）=Ji（x（ti）,x′（t））,i=1,2,…,k,x（0）=0=x（1）-αx（η）,where 0〈η〈1,α∈R,and f：[0,1]×R×R→R,Ii：R×R→R,Ji：R×R→R（i=1,2,…,k）are continuous. Our results is new and different from previous results. In particular, we obtain the Green function of the problem, which makes the problem simpler.展开更多
In this paper,we are concerned with the existence of multiple positive solutions to a second-order three-point boundary value problem on the half-line.The results are obtained by the Leggett-Williams fixed point theorem.
A class of third-order three-point boundary value problems is considered, where the nonlinear term is a Caratheodory function. By introducing a height function and considering the imtegration of this height function, ...A class of third-order three-point boundary value problems is considered, where the nonlinear term is a Caratheodory function. By introducing a height function and considering the imtegration of this height function, an existence theorem of solution is proved when the limit growth function exists. The main tools are the Lebesgue dominated convergence theorem and the Schauder fixed point theorem.展开更多
Monotone sequences are constructed that converge to the ex tremal solutions of second order three point boundary value problems when the functions involved do not possess any monotone properties.
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
This paper discusses both the nonexistence of positive solutions for second-order three-point boundary value problems when the nonlinear term f（t, x, y） is superlinear in y at y = 0 and the existence of multiple pos...This paper discusses both the nonexistence of positive solutions for second-order three-point boundary value problems when the nonlinear term f（t, x, y） is superlinear in y at y = 0 and the existence of multiple positive solutions for second-order three-point boundary value problems when the nonlinear term f（t, x,y） is superlinear in x at ＋∞.展开更多
In this paper,we consider the discrete boundary value problem of the type{∆u1=0=∆un-1,∇(t_(k)^(N-1))φ(∆uk))+t_(k)^(N-1)fk(t_(k),u_(k),∆_(uk))=0,2≤k≤n-1,whereφ:(-a,a)→R,0<a<∞,is an increasing homeomorphism ...In this paper,we consider the discrete boundary value problem of the type{∆u1=0=∆un-1,∇(t_(k)^(N-1))φ(∆uk))+t_(k)^(N-1)fk(t_(k),u_(k),∆_(uk))=0,2≤k≤n-1,whereφ:(-a,a)→R,0<a<∞,is an increasing homeomorphism withφ(0)=0,such aφis called singular,N≥1,n≥3 are integers,tk are the grid points,uk:=u(tk),k=1,2,...,n,∇is the backward difference operator defined by∆uk=uk-uk-1,△is the forward difference operator defined by△uk=uk+1-uk,fk(2≤k≤n-1)are continuous functions.We prove the existence of solutions to this problem by employing the sign condition,the continuation lemma and the upper and lower solutions,respectively.On this basis,we also establish the Ambrosetti-Prodi type results for it.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
Some existence theorems of three-point boundary value problems for a class ofthree order differential inclusions are obtained by means of the topological degree theory forset-valued mappings and an improved Wirtinger...Some existence theorems of three-point boundary value problems for a class ofthree order differential inclusions are obtained by means of the topological degree theory forset-valued mappings and an improved Wirtinger’s inequality. The results, even restrictedto the case of differential equations, have generized and improved on the related results in[1]. Particularlyt a problem raised in Remark 5 in if] is answered definitely.展开更多
Ⅰ. INTRODUCTIONThis note presents some criteria which guarantee the existence and uniqueness of solutions of two-point and three-point boundary value problems
In this paper, we investigate the existence of nontrivial solutions for some superlinear second order three-point boundary value problems by applying new fixed point theorems in ordered Banach spaces with the lattice ...In this paper, we investigate the existence of nontrivial solutions for some superlinear second order three-point boundary value problems by applying new fixed point theorems in ordered Banach spaces with the lattice structure derived by Sun and Liu.展开更多
In this paper we investigate the existence of solutions of the nonhomogeneous three-point boundaryvalue problem We search for solutions of the above problem in the Banach space of continuous functions C（[O, 1], E）...In this paper we investigate the existence of solutions of the nonhomogeneous three-point boundaryvalue problem We search for solutions of the above problem in the Banach space of continuous functions C（[O, 1], E） with the Pettis integrability assumptions imposed on $. Some classes of Pettis-integrable functions are described in the paper and exploited in the proofs of main results. We stress on a class of pseudo-solutions of considered problem. Our results extend previous results of the same type for both Bochner and Pettis integrability settings. Similar results are also proved for differential inclusions i.e. when f is a multivalued function.展开更多
The singularly perturbed elliptic equation boundary value problem with turning point is considered. Using the method of multiple scales and the comparison theorem, the asymptotic behavior of solution for the boundary ...The singularly perturbed elliptic equation boundary value problem with turning point is considered. Using the method of multiple scales and the comparison theorem, the asymptotic behavior of solution for the boundary value problem is studied.展开更多
In this paper, by using Leray-Schauder degree theory, we establish the existence and uniqueness theorems for some higher order nonlinear three-point boundary value problems.
This paper studies the existence of nontrivial solution to a nonlinear fourthorder three-point boundary value problem,where the nonlinear term is a strong Carathodory function and contains all order derivatives of unk...This paper studies the existence of nontrivial solution to a nonlinear fourthorder three-point boundary value problem,where the nonlinear term is a strong Carathodory function and contains all order derivatives of unknown function.By introducing a height function of nonlinear term on some bounded set and considering the integration of the height function,some existence results are obtained.展开更多
By establishing equivalent fixed point theorem, the boundary value problems of p Laplace equations with finite time delay are studied. It’s the first time that the functional differential equation is discussed w...By establishing equivalent fixed point theorem, the boundary value problems of p Laplace equations with finite time delay are studied. It’s the first time that the functional differential equation is discussed with p Laplacian. The topological degree and fixed point theorem on cone are used to prove the existence of solution and positive solution. The conditions are all easy to check.展开更多
The existence of solutions for singular nonlinear two point boundary value problems subject to Sturm Liouville boundary conditions with p Laplacian operators is studied by the method of upper and lower solution...The existence of solutions for singular nonlinear two point boundary value problems subject to Sturm Liouville boundary conditions with p Laplacian operators is studied by the method of upper and lower solutions. The proof is based on an application of Schauder’s fixed point theorem to a modified problem whose solutions are that of the original one. At the same time, Arzela Ascoli theorem is used to prove that the defined operator N is a compact map.展开更多
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.
基金Supported by the Foundation of the Office of Science and Technology of Henan(122102310373)Supported by the NSF of Education Department of Henan Province(12B110025)
文摘In this paper, by using the fixed-point index theory, we study the existence of sign-changing solution of some three-point boundary value problems {y ''(t) + f(y) = 0, t ∈ [0, 1], y' (0) = 0, y(1) = αy(η), where 0 < α < 1, 0 < η < 1, f : R → R is continuous, strictly increasing and f(0) = 0.
基金Supported by the National Natural Science Foundation of China(10371006)
文摘We study the existence of solutions to the second order three-point boundary value problem：{x″（t）＋f（t,x（t）,x′（t））=0,t≠ti,△x（ti）=Ii（x（ti）,x′（ti））,i=1,2,…,k,△x′（ti）=Ji（x（ti）,x′（t））,i=1,2,…,k,x（0）=0=x（1）-αx（η）,where 0〈η〈1,α∈R,and f：[0,1]×R×R→R,Ii：R×R→R,Ji：R×R→R（i=1,2,…,k）are continuous. Our results is new and different from previous results. In particular, we obtain the Green function of the problem, which makes the problem simpler.
基金Supported by the NNSF of China(10871116)Supported by the NSFSP of China(ZR2010AM005)
文摘In this paper,we are concerned with the existence of multiple positive solutions to a second-order three-point boundary value problem on the half-line.The results are obtained by the Leggett-Williams fixed point theorem.
文摘A class of third-order three-point boundary value problems is considered, where the nonlinear term is a Caratheodory function. By introducing a height function and considering the imtegration of this height function, an existence theorem of solution is proved when the limit growth function exists. The main tools are the Lebesgue dominated convergence theorem and the Schauder fixed point theorem.
文摘Monotone sequences are constructed that converge to the ex tremal solutions of second order three point boundary value problems when the functions involved do not possess any monotone properties.
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.
基金Supported by the National Natural Science Foundation of China(No.10571111)the fund of Shandong Education Committee(J07WH08).
文摘This paper discusses both the nonexistence of positive solutions for second-order three-point boundary value problems when the nonlinear term f（t, x, y） is superlinear in y at y = 0 and the existence of multiple positive solutions for second-order three-point boundary value problems when the nonlinear term f（t, x,y） is superlinear in x at ＋∞.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1236104012461035)+1 种基金the Outstanding Youth Fund of Gansu Province(Grant No.24JRRA121)the Scientific Research Ability Improvement Program for Young Teachers of Northwest Normal University(Grant No.NWNU-LKQN2021-17)。
文摘In this paper,we consider the discrete boundary value problem of the type{∆u1=0=∆un-1,∇(t_(k)^(N-1))φ(∆uk))+t_(k)^(N-1)fk(t_(k),u_(k),∆_(uk))=0,2≤k≤n-1,whereφ:(-a,a)→R,0<a<∞,is an increasing homeomorphism withφ(0)=0,such aφis called singular,N≥1,n≥3 are integers,tk are the grid points,uk:=u(tk),k=1,2,...,n,∇is the backward difference operator defined by∆uk=uk-uk-1,△is the forward difference operator defined by△uk=uk+1-uk,fk(2≤k≤n-1)are continuous functions.We prove the existence of solutions to this problem by employing the sign condition,the continuation lemma and the upper and lower solutions,respectively.On this basis,we also establish the Ambrosetti-Prodi type results for it.
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Some existence theorems of three-point boundary value problems for a class ofthree order differential inclusions are obtained by means of the topological degree theory forset-valued mappings and an improved Wirtinger’s inequality. The results, even restrictedto the case of differential equations, have generized and improved on the related results in[1]. Particularlyt a problem raised in Remark 5 in if] is answered definitely.
基金Project supported partially by the National Natural Science Foundation of China.
文摘Ⅰ. INTRODUCTIONThis note presents some criteria which guarantee the existence and uniqueness of solutions of two-point and three-point boundary value problems
基金Supported in part by the National Natural Science Foundation of China under Grant No.11571207Research Award Fund for Outstanding Young Scientists of Shandong Province under Grant No.BS2012SF022
文摘In this paper, we investigate the existence of nontrivial solutions for some superlinear second order three-point boundary value problems by applying new fixed point theorems in ordered Banach spaces with the lattice structure derived by Sun and Liu.
文摘In this paper we investigate the existence of solutions of the nonhomogeneous three-point boundaryvalue problem We search for solutions of the above problem in the Banach space of continuous functions C（[O, 1], E） with the Pettis integrability assumptions imposed on $. Some classes of Pettis-integrable functions are described in the paper and exploited in the proofs of main results. We stress on a class of pseudo-solutions of considered problem. Our results extend previous results of the same type for both Bochner and Pettis integrability settings. Similar results are also proved for differential inclusions i.e. when f is a multivalued function.
文摘The singularly perturbed elliptic equation boundary value problem with turning point is considered. Using the method of multiple scales and the comparison theorem, the asymptotic behavior of solution for the boundary value problem is studied.
文摘In this paper, by using Leray-Schauder degree theory, we establish the existence and uniqueness theorems for some higher order nonlinear three-point boundary value problems.
文摘This paper studies the existence of nontrivial solution to a nonlinear fourthorder three-point boundary value problem,where the nonlinear term is a strong Carathodory function and contains all order derivatives of unknown function.By introducing a height function of nonlinear term on some bounded set and considering the integration of the height function,some existence results are obtained.
文摘By establishing equivalent fixed point theorem, the boundary value problems of p Laplace equations with finite time delay are studied. It’s the first time that the functional differential equation is discussed with p Laplacian. The topological degree and fixed point theorem on cone are used to prove the existence of solution and positive solution. The conditions are all easy to check.
文摘The existence of solutions for singular nonlinear two point boundary value problems subject to Sturm Liouville boundary conditions with p Laplacian operators is studied by the method of upper and lower solutions. The proof is based on an application of Schauder’s fixed point theorem to a modified problem whose solutions are that of the original one. At the same time, Arzela Ascoli theorem is used to prove that the defined operator N is a compact map.
