Existence of Positive Solutions for Nonlinear Second-Order Impulsive Boundary Value Problems on Time Scales

This paper is concerned with the existence of positive solutions of second-order impulsive boundary value problem with integral boundary conditions on time scales. Existence results of at least three positive solutions are established via a new fixed point theorem in a cone. Also, an example is given to illustrate the effectiveness of our result.     

一类非线性离散系统的同宿解的存在性

应用临界点理论讨论一类二阶非线性离散系统在一定条件下非零同宿解的存在性,得到一个非零同宿解存在性的条件.     

随机二阶多值周期问题解的存在性

本文研究了随机二阶多值周期问题解的存在性,在非常一般的假定下建立了凸和非凸问题解的存在性定理,并给出了在随机周期反馈控制系统中的应用．     

奇异微分方程和差分方程Sturm-Liouville边值问题正解的存在唯一性

利用混合单调算子,研究了微分方程和差分方程的Sturm-Liouville边值问题,得到了一个正解存在唯一的充分条件.     

非线性二阶微分系统正解的存在性

考虑二阶微分系统边值问题[JB({]x″(t)+λ f(t,x(t),y(t))=0,\=y″(t)+μ g(t,x(t),y(t))=0,\ 00, f, g:［0,1］×［0,∞)×［0,∞)→R连续. 突破了以往文献要求非线性项 f, g非负的限制，运用锥上的一个不动点定理,在半正的情形下建立了问题正解的存在性     

一类二阶三点非线性边值问题的正解存在性与多解性

利用Krasnosel’skii锥拉伸与锥压缩型不动点定理考察了一类二阶三点非线性边值问颗的正解存在性、 非存性与多解性。     

关于一个二阶非线性中立时滞微分方程的非振荡解的存在性

A new second-order nonlinear neutral delay differential equation r（t） x（t） ＋ P（t）x（t-τ） ＋ cr（t） x（t）-x（t-τ） ＋ F t,x（t-σ1）,x（t-σ2）,...,x（t-σn） = G（t）,t ≥ t0,where τ 0,σ1,σ2,...,σn ≥ 0,P,r ∈ C（[t0,＋∞）,R）,F ∈ C（[t0,＋∞）×Rn,R）,G ∈ C（[t0,＋∞）,R） and c is a constant,is studied in this paper,and some sufficient conditions for existence of nonoscillatory solutions for this equation are established and expatiated through five theorems according to the range of value of function P（t）.Two examples are presented to illustrate that our works are proper generalizations of the other corresponding results.Furthermore,our results omit the restriction of Q1（t） dominating Q2（t）（See condition C in the text）.     

共振情形下二阶多点边值问题解的存在性

运用Mawhin重合度理论,讨论了共振情形下一类二阶多点边值问题解的存在性,在算子L满足Ker L=2的条件下,获得了该问题解的存在性结果.     

二阶微分方程反周期边值问题解的存在性

在这篇文章中,我们考虑了一类非线性二阶常微分方程反周期边值问题．利用上下解方法结合单调迭代技巧,我们得到了解的存在性结果．     

二阶Sturm-Liouville特征值问题解的存在与非存在性

讨论了二阶Sturm-Liouville特征值边值问题解的存在性与非存在性,得到了边值问题至少有一个正解的特征值λ的存在区间的结论.进一步,给出了边值问题没有正解的特征值存在区间.     

与 p-Laplacian 算子相关的非线性Neumann边值问题解的存在性

Using perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we present the abstract results on the existence of solutions of one kind nonlinear Neumann boundary value problems related to p-Laplacian operator. The equation discussed in this paper and the method used here extend and complement some of the previous work.     

非线性椭圆型边值问题解的存在性

Hilbert空间方法被用于一类二阶半线性椭圆型边值问题并得出了某些条件下的解的存在性.     

二阶脉冲微分方程三点边值问题解的存在性

讨论二阶脉冲微分方程三点边值问题解的存在性 ,所使用的方法是 Schauder不动点定理和压缩映射原理 .     

Existence and Multiplicity of Solutions of Second-Order Difference Boundary Value Problems

This paper concerns the existence and multiplicity of solutions of second-order difference boundary value problems. Under the assumptions which guarantee the existence of at least one nontrivial solution of the homogeneous problem, we obtain the existence of exactly three solutions of the nonhomogeneous problem with some other suitable conditions.     

Existence of Positive Solutions for Second-Order m-Point Boundary Value Problems on Time Scales

This paper investigates thc existence of positive solutions of the m-point boundary value problem for second-order dynamic equations on time scales, and obtain the result that the problem has at least one positive solution by using functional-type cone expansion-compression fixed point theorem.     

On Existence of Infinitely Many Homoclinic Solutions

 In this note we prove some sufficient condition for the existence of homoclinic solutions in nonautonomous ODE’s. As an application we show that there exist infinitely many (geometrically distinct) homoclinic solutions to the trivial 0 solution in the planar system

Existence of Positive Solutions for Second-Order Impulsive Boundary Value Problems on Time Scales

In this paper, by using Leray–Schauder fixed-point theorem, Avery–Henderson fixed-point theorem and Leggett–Williams fixed-point theorem, respectively, we investigate the conditions for the existence of at least one, two and three positive solutions to nonlinear second-order impulsive boundary value problems on time scales.     

非线性椭圆型问题爆炸解的存在性

应用摄动方法,古典上、下解方法,对含更广泛非线性项的问题(P-)-△u=k(x)f(u)-｜↓△u｜^q,x∈Ω,u｜δΩ= ∞到爆炸解的存在性．特别允许非线性项的系数k(x)不仅在Ω的子区域上可恒为零,而且在Ω上适当无界;而对问题(P )△u=k(x)f(u) ｜↓△u｜^q,x∈Ω,u｜δΩ= ∞仅得到了当k(x)∈C^a(Ω^-)且k(x)＞0,x∈Ω^-时爆炸解的存在性．