关于几类非线性脉冲微分方程解的存在性研究

发布时间：2018-04-12 11:35

本文选题：脉冲 + 分数阶积分-微分方程　；参考：《曲阜师范大学》2017年硕士论文

【摘要】：非线性泛函分析作为数学中一个既有深刻理论又有广泛应用的研究领域,它以自然界中出现的非线性问题为背景,建立了处理非线性问题的若干一般性理论和方法.近年来,非线性微分方程已经引起国内外数学界及自然科学界的高度重视,成为国际研究热点方向之一.脉冲微分方程在化学、工程、种群动态和经济学等诸多领域得到以广泛应用.许多数学家应用非线性分析工具得到了非线性脉冲微分方程解的存在性和解的性质等结论.本文主要研究几类非线性脉冲微分方程解的存在性.本文共分为以下三章:第一章,研究带有常系数的分数阶脉冲积分-微分方程反周期边值问题运用Banach压缩映射原理和Krasnoselskii不动点定理,得到上述问题解的存在性和唯一性.第二章,研究带有反周期边界条件的分数阶脉冲q-差分方程运用Leray-Schauder二择一定理和Banach压缩映射原理研究了解的存在性和唯一性.第三章,研究带有积分边界条件的二阶脉冲微分方程组在非线性项允许变号的情况下,运用了双锥上的Krasnoselskii不动点定理得到了上述问题两个非负解的存在性.
[Abstract]:Nonlinear functional analysis (NFA) is a deep theory and widely applied research field in mathematics. Based on the nonlinear problems in nature, some general theories and methods for dealing with nonlinear problems are established.In recent years, nonlinear differential equations have attracted great attention in the field of mathematics and natural science at home and abroad, and have become one of the hot international research directions.Impulsive differential equations are widely used in many fields, such as chemistry, engineering, population dynamics and economics.Many mathematicians have obtained the existence and properties of solutions of nonlinear impulsive differential equations by using nonlinear analysis tools.In this paper, we study the existence of solutions for some nonlinear impulsive differential equations.This paper is divided into three chapters: in Chapter 1, we study the anti-periodic boundary value problems of fractional impulsive integro-differential equations with constant coefficients. By using the Banach contraction mapping principle and Krasnoselskii fixed point theorem, we obtain the existence and uniqueness of the solutions above.In chapter 2, we study the existence and uniqueness of solutions for fractional impulsive q-difference equations with counterperiodic boundary conditions by using Leray-Schauder 's bioptional theorem and Banach contraction mapping principle.In chapter 3, we study the existence of two nonnegative solutions for second order impulsive differential equations with integral boundary conditions by using the Krasnoselskii fixed point theorem on two cones.
【学位授予单位】：曲阜师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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