發(fā)布時間：2018-10-29 14:44

【摘要】：微分方程是非線性泛函分析的一個重要部分,其中,分數(shù)階微分方程解的存在性問題是非線性泛函分析中研究最活躍的領域之一.本文中主要利用Banach壓縮映射原理,Lipschitz條件.Krasnoselskii不動點定理及錐拉伸壓縮不動點定理研究了分數(shù)階微分方程解的存在性.本文共分為二章:在第一章中,主要應用上下解方法和單調(diào)迭代方法,得到了下列帶有積分邊值條件的分數(shù)階微分方程極解的存在性,其中cD0+α是α階Cαputo分數(shù)階導數(shù),2 α 3, 0 λ 1, f : [0,1] ×[0,∞) → [0,∞)是連續(xù)函數(shù).在第二章中,我們主要研究了下列分數(shù)階微分方程解的存在性問題,其中Dv+v是Riemann - Liouville分數(shù)階導數(shù),4, 0η≤1,0≤ληv/v 1,f (t,u 是連續(xù)的,且在某區(qū)間是變號的.這一章中主要應用Lipschitz條件及Krasnoselskii不動點定理得到了分數(shù)階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 偽 is the fractional derivative of order C 偽 puto, 2 偽 3. 0 位 1, f: [0 1] 脳 [0, 鈭，

本文編號：2297996