【作者】 李敏；

【导师】 周树清；

【作者基本信息】 湖南师范大学 ， 应用数学， 2015， 硕士

【摘要】 关于时标理论的研究起源于1988年的德国数学家Hilger,之后时标上动力方程引起了越来越多学者的广泛关注.原因有两方面：从理论上说,时标分析理论能在连续分析和离散分析之间建立桥梁,能够统一连续问题和离散问题；从应用上看,时标动力方程有重要的应用价值,例如，不同季节昆虫种群的活动期和休眠期可用时标上的动力方程描述.本文主要利用Krasnosel’ skii不动点定理Schauder不动点定理讨论了时标上几类动力方程边值问题解的存在性.全文共分为四章.第一章介绍了本课题产生的历史背景以及本文的主要工作.第二章介绍了本文的预备知识.第三章讨论了时标上一类奇异四阶三点边值问题正解的存在性.利用Krasnosel’ skii不动点定理得到了上述边值问题至少存在一个正解.第四章讨论了时标上一类奇异三阶m点边值问题非平凡解的存在性.利用Schauder不动点定理得到了上述边值问题正解的存在性.更多还原

【Abstract】 The theory of time scales was introduced by Stefan Hilger in 1988.After that more and more scholars take an interest in dynamic equations on time scales.There are two reasons. From the theoretical point of view, the time scales analysis theory can build bridges between continuous and dispersion. From the application point of view, dynamic equations on time scales has important applications. For example, the activities of insect populations in the different seasons and resting can be described by the dynamic equations on time scales.This paper mainly discusses the existence of solutions for several kinds of boundary value problems of nonlinear dynamic equations on time scales by using the Krasnosel’skii fixed point theorem and Schauder fixed point theorem. There are three chapters in this paper.In Chapter 1, introduce issues arising from the historical background and main tasks of this article.In Chapter 2, introduce preliminary knowledge of this article.In Chapter 3, discuss the existence of positive solutions of the following sin-gular BVP This paper obtains existence of positive solution by using the Krasnosel’skii fixed point theorem.In Chapter 4, studies the existence of positive solution for a singular third-order m point BVP on time scalesThis paper obtains existence of positive solution by using Schauder fixed point theory.更多还原