时标上几类积分边值问题多解性研究

发布时间：2018-01-05 14:37

本文关键词：时标上几类积分边值问题多解性研究　出处：《云南大学》2015年硕士论文　论文类型：学位论文

【摘要】：本论文就时标上的积分边值问题多解性作出一些研究,并得到了一系列新的结果. 本论文的组织结构安排如下, 第一章,主要介绍本文的研究背景及研究价值.第二章主要介绍相关概念、定义及定理. 第三章,研究如下时标上三阶带p-Laplacian算子动力方程积分边值问题的多个正解的存在性：其中.令ρ:=ad+ac+bc区间[0,1]T：-[0,1]∩T,并且0,1∈T,本文用φp(u)表示p-Laplacian算子,即Φp(u)=|u|p-2u,p1,(Φp)-1=Φq,1/p+1/q=1通过利用Legggt-Williams不动点定理的推广定理获得了时标上三阶带p-Laplacian算子的动力方程积分边值问题至少存在三个正解的判定定理；第四章,考虑以下时标上带积分边值问题三阶非线性微分方程的多解性：其中,区间[0,1]T：=[0.1]∩T,并且0,1∈T,φ：R→R连续同胚正同态,并且满足O(0)=0.并根据Leggtt-Williams不动点定理的推广定理,得到了时标上三阶动力方程积分边值问题至少存在三个正解的充分条件.
[Abstract]:In this paper, we make some research on the multi solution of the integral boundary value problem on the time scale, and get a series of new results.
The organizational structure of this paper is arranged as follows.
The first chapter mainly introduces the research background and value of the study. The second chapter mainly introduces the related concepts, definitions and theorems.
The third chapter, the following research on time scales of three order p-Laplacian operator with dynamic equations with integral boundary value problems of the existence of multiple positive solutions: one. Make p: =ad+ac+bc T and 0,1 [0,1]T:-[0,1] interval, and T, with the P diameter (U) said that with the p-Laplacian operator, P (U) =|u|p-2u, P1 (P) -1=, Phi Q, 1/p+1/q=1 by using the theorem of Legggt-Williams theorem is obtained when the underlying problem has at least three positive solutions theorems of integral dynamic equation with p-Laplacian operator on the three order boundary value;
The fourth chapter, consider the following multiple solutions with integral boundary value problem of three order nonlinear differential equations on scales: the range of [0,1]T:=[0.1] T, and 0,1, T, R, R: Phi continuous homeomorphism is homomorphism, and meet the O (0) =0. and according to the extension of Leggtt-Williams fixed point theorem theorem, obtain the sufficient conditions for the existence of three positive solutions of the boundary integral three order dynamic equation on time scales.

【学位授予单位】：云南大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175.8

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