【摘要】：微分方程是非線性泛函分析的一個(gè)重要部分,其中,分?jǐn)?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(lǐng)域之一.本文中主要利用Banach壓縮映射原理,Lipschitz條件.Krasnoselskii不動(dòng)點(diǎn)定理及錐拉伸壓縮不動(dòng)點(diǎn)定理研究了分?jǐn)?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(yīng)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?jǐn)?shù)階微分方程極解的存在性,其中cD0+α是α階Cαputo分?jǐn)?shù)階導(dǎo)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?jǐn)?shù)階微分方程解的存在性問題,其中Dv+v是Riemann - Liouville分?jǐn)?shù)階導(dǎo)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(hào)的.這一章中主要應(yīng)用Lipschitz條件及Krasnoselskii不動(dòng)點(diǎn)定理得到了分?jǐn)?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(hào)：2297996