两类微分方程三点边值问题的研究
发布时间：2018-11-27 11:35
【摘要】：本文研究的是两类微分方程三点边值问题,在满足Legget t-Williams不动点定理的条件下,分别探讨并证明了二阶脉冲时滞微分方程及分数阶微分方程的三点边值问题的三个对称正解的存在性,并给出了数值举例.文章的叙述结构安排如下:第一章介绍研究课题的背景、研究现状及意义,以及本文的研究方法、主要结果:第二章主要研究二阶脉冲时滞微分方程的三点边值问题的三个对称正解的存在性并给出了数值举例;第三章主要研究了分数阶时滞微分方程的三点边值问题的三个对称正解的存在性并给出了数值举例.
[Abstract]:In this paper, we study two kinds of three-point boundary value problems for differential equations. Under the condition of satisfying the Legget t-Williams fixed point theorem, The existence of three symmetric positive solutions for three point boundary value problems of second order impulsive delay differential equations and fractional order differential equations are discussed and proved, and numerical examples are given. The narrative structure of the article is as follows: the first chapter introduces the background of the research topic, the status quo and significance of the research, as well as the research methods of this paper. The main results are as follows: in the second chapter, the existence of three symmetric positive solutions for the three-point boundary value problems of second order impulsive delay differential equations is studied and numerical examples are given. In chapter 3, the existence of three symmetric positive solutions for three point boundary value problems of fractional delay differential equations is studied and numerical examples are given.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175.8
本文编号：2360599
[Abstract]:In this paper, we study two kinds of three-point boundary value problems for differential equations. Under the condition of satisfying the Legget t-Williams fixed point theorem, The existence of three symmetric positive solutions for three point boundary value problems of second order impulsive delay differential equations and fractional order differential equations are discussed and proved, and numerical examples are given. The narrative structure of the article is as follows: the first chapter introduces the background of the research topic, the status quo and significance of the research, as well as the research methods of this paper. The main results are as follows: in the second chapter, the existence of three symmetric positive solutions for the three-point boundary value problems of second order impulsive delay differential equations is studied and numerical examples are given. In chapter 3, the existence of three symmetric positive solutions for three point boundary value problems of fractional delay differential equations is studied and numerical examples are given.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175.8
【参考文献】
相关期刊论文 前2条
1 胡卫敏;伊磊;陈维;;一类分数阶微分方程三点边值问题的多重正解[J];东北师大学报(自然科学版);2011年02期
2 钟文勇;;分数阶微分方程多点边值问题的正解[J];吉首大学学报(自然科学版);2010年01期
，本文编号：2360599
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