带有非线性边界条件的微分方程解的存在性

发布时间：2018-10-29 14:44

【摘要】：微分方程是非线性泛函分析的一个重要部分,其中,分数阶微分方程解的存在性问题是非线性泛函分析中研究最活跃的领域之一.本文中主要利用Banach压缩映射原理,Lipschitz条件.Krasnoselskii不动点定理及锥拉伸压缩不动点定理研究了分数阶微分方程解的存在性.本文共分为二章:在第一章中,主要应用上下解方法和单调迭代方法,得到了下列带有积分边值条件的分数阶微分方程极解的存在性,其中cD0+α是α阶Cαputo分数阶导数,2 α 3, 0 λ 1, f : [0,1] ×[0,∞) → [0,∞)是连续函数.在第二章中,我们主要研究了下列分数阶微分方程解的存在性问题,其中Dv+v是Riemann - Liouville分数阶导数,4, 0η≤1,0≤ληv/v 1,f (t,u 是连续的,且在某区间是变号的.这一章中主要应用Lipschitz条件及Krasnoselskii不动点定理得到了分数阶微分方程解的存在性.
[Abstract]:Differential equations are an important part of nonlinear functional analysis. Among them, the existence of solutions of fractional differential equations is one of the most active research fields in nonlinear functional analysis. In this paper, the existence of solutions of fractional differential equations is studied by using Banach contraction mapping principle, Lipschitz condition, Krasnoselskii fixed point theorem and cone stretching contraction fixed point theorem. This paper is divided into two chapters: in the first chapter, by using the upper and lower solution method and monotone iterative method, we obtain the existence of extreme solutions of fractional differential equations with integral boundary value conditions, where cD0 伪 is the fractional derivative of order C 伪 puto, 2 伪 3. 0 位 1, f: [0 1] 脳 [0, 鈭，

本文编号：2297996