次线性奇异三点边值问题的正解

该文主要研究二阶次线性奇异三点边值问题的正解的存在性,利用上下解方法和比较定理给出了C[0,1] 和 C¹[0,1]$ 正解存在的充分必要条件,其中的非线性项 f(t,x) 可以在 x=0, t=0 和 t=1 处奇异.     

BOUNDARY VALUE PROBLEM FOR NON-LINEAR SECOND ORDER ORDINARY DIFFERENTIAL EQUATION WITH DISCONTINUOUS TERMS IN BANACH SPACE

By using upper and lower solutions and fixed point theorem we give the existence theorem of non-linear second order ordinary differential equation with discontinuous terms in Banach Space.     

一类四阶边值问题的分析

该文考虑的四阶边值问题，可用于描述飞机、轮船及建筑物的结构模型。由经典的分析方法，如辅助的截断函数，Schauder不动点定理，作者首先提出一种改进的上、下解方法；然后，利用二阶齐次边值问题的第一特征函数，构造出具体的上解，同时取0为相应下解，在更一般的假设下得到正解的存在性； 最后探讨了右端项f(x,y,z)在y=0奇异的情形。     

一类四阶两点边值问题正解的存在性

运用上下解方法及拓扑度理论讨论了非齐次边界条件下四阶两点边值问题u″″(t)=f(u(t)),t∈(0,1),u(0)=u″(0)=u″(1)=0,u(1)=λ,其中λ＞0为参数,f∈C([0,+∞),[0,+∞)).在非线性项满足一定的增长条件下,获得了上述问题存在正解时λ的取值范围.     

具有积分边界条件的四阶奇异特征值问题的正解

本文研究一类具有积分边界条件的四阶奇异特征值问题正解的存在性,非线性项f(t,u)允许在t=0和/或t=1和u=0处奇异.首先给出一个新的比较定理,然后构造奇异特征值问题的上下解,最后运用Schauder不动点定理获得了当f(t,u)关于u是减的情况下正解的存在性,给出了处理f(t,u)允许在u=0处奇异的方法,可以处理f(t,u)在u=0处奇异的方法并不多见.     

二阶时滞微分方程边值问题的上下解方法

主要利用上下解方法和Schauder不动点定理,研究一类二阶时滞微分方程边值问题的正解存在性.为了验证结论的正确性,本文在结尾部分给出了两个例子.     

负指数Emden Fowler方程奇异边值问题的正解

本文利用上下解方法和不动点理论给出了负指数Ｅｍｄｅｎ Ｆｏｗｌｅｒ方程奇异边值问题有Ｃ［０，１］和Ｃ１［０，１］正解存在的充分必要条件．     

负指数EmdenFowler方程奇异边值问题的正解

本文利用上下解方法和不动点理论给出了负指数ＥｍｄｅｎＦｏｗｌｅｒ方程奇异边值问题有Ｃ［０，１］和Ｃ１［０，１］正解存在的充分必要条件．     

一类四阶次线性奇异边值问题的正解

本文利用极大值原理和通过构造上下解给出了一类四阶次线性微分方程的奇异边值问题有C2[0,1]和C3[0,1]正解存在的充分必要条件.     

Banach空间二阶周期边值问题的一种拟上下解方法

利用比较结果,通过构造L-拟上下解的单调迭代过程,在L-拟上下解反序的情形下,研究了Banach空间二阶周期边值问题解的存在性,并获得该问题解的存在性与唯一性结果.     

SOME NEW RESULTS FOR NONLINEAR BOUNDARY VALUE PROBLEMS OF MIXED TYPE INTEGRODIFFERENTIAL EQUATION

In this paper we give the existence and uniqueness of solutions for boundary value problems of the form u" = f(t, u,u', T1u,T2u), g(u(0),u(1)) = 0, h(w(0), u(1),u'(0), u'(1)) = 0 by means of the upper and lower solution method.     

Existence and Comparison Results for Difference φ-Laplacian Boundary Value Problems with Lower and Upper Solutions in Reverse Order

This paper is devoted to the study of the existence and comparison results for nonlinear difference φ-Laplacian problems with mixed, Dirichlet, Neumann, and periodic boundary value conditions. We deduce existence of extremal solutions of periodic and Neumann boundary value problems lying between a pair of lower and upper solutions given in reverse order. We prove the optimality of some assumptions in φ.     

奇异二阶微分方程积分边值问题正解的存在唯一性

利用上下解方法结合极值原理研究一类带积分边值条件的奇异二阶微分方程正解的存在性以及唯一性,给出了$C[0,1]$和$C^1[0,1]$正解存在唯一的一个充分条件.非线性项允许在$t=0,1$ 和$x=0$处具有奇异性.     

四阶奇异边值问题的正解

本文利用上下解方法和极大值原理给出了四阶微分方程的奇异边值问题有C2[0,1]和C3[0,1]正解存在的充分必要条件.     

Banach空间中二阶微分方程的周期边值问题

本文在Banach空间中研究了二阶非线性微分方程的周期边值问题:-u″=f(t,u),u(0)= u(2π),u′(0)=u′,(2π)在上下解反向给定时,利用半序理论和新的比较原理,证明了该周期边值问题最小解和最大解的存在性,解的唯—性,并给出了唯一解的近似迭代序列的误差估计式．     

一类二阶泛函微分方程的周期边值问题

讨论了一类二阶泛函微分方程的周期边值问题,给出了上、下解的一个新的概念,并且得到了一个新的比较结果.同时,修正了相关文献中的一个错误.     

一类高阶奇异边值问题正解存在的充分必要条件

利用上下解方法和极大值原理给出了一类高阶微分方程的奇异边值问题正解存在的充分必要条件．     

A class of boundary value problems for first-order impulsive integro-differential equations with deviating arguments

This paper is concerned with a class of boundary value problems for nonlinear mixed impulsive integro-differential equations with deviating arguments. We establish a new comparison principle and use the method of upper and lower solutions together with the monotone iterative technique. Under suitable conditions, we obtain the existence results of extremal solutions for the problems. An example is also given to illustrate our results.     

Existence and qualitative features of entire solutions for delayed reaction diffusion system: the monostable case

The paper is concerned with the existence and qualitative features of entire solutions for delayed reaction diffusion monostable systems. Here the entire solutions mean solutions defined on the $ (x,t)\in\mathbb{R}^{N+1} $. We first establish the comparison principles, construct appropriate upper and lower solutions and some upper estimates for the systems with quasimonotone nonlinearities. Then, some new types of entire solutions are constructed by mixing any finite number of traveling wave fronts with different speeds $ c\geq c_* $ and propagation directions and a spatially independent solution, where $c_*>0$ is the critical wave speed. Furthermore, various qualitative properties of entire solutions are investigated. In particularly, the relationship between the entire solution, the traveling wave fronts and a spatially independent solution are considered, respectively. At last, for the nonquasimonotone nonlinearity case, some new types of entire solutions are also investigated by introducing two auxiliary quasimonotone controlled systems and establishing some comparison theorems for Cauchy problems of the three systems.     

二阶奇异非线性边值条件的上下解方法

本文利用上下解方法,讨论奇性边值问题(py’)’+ p(t)q(t)f(t,y,py’)=0,0相似文献