本文選題：脈沖 + 分數(shù)階積分-微分方程��； 參考：《曲阜師范大學》2017年碩士論文

【摘要】：非線性泛函分析作為數(shù)學中一個既有深刻理論又有廣泛應用的研究領域,它以自然界中出現(xiàn)的非線性問題為背景,建立了處理非線性問題的若干一般性理論和方法.近年來,非線性微分方程已經(jīng)引起國內(nèi)外數(shù)學界及自然科學界的高度重視,成為國際研究熱點方向之一.脈沖微分方程在化學、工程、種群動態(tài)和經(jīng)濟學等諸多領域得到以廣泛應用.許多數(shù)學家應用非線性分析工具得到了非線性脈沖微分方程解的存在性和解的性質(zhì)等結論.本文主要研究幾類非線性脈沖微分方程解的存在性.本文共分為以下三章:第一章,研究帶有常系數(shù)的分數(shù)階脈沖積分-微分方程反周期邊值問題運用Banach壓縮映射原理和Krasnoselskii不動點定理,得到上述問題解的存在性和唯一性.第二章,研究帶有反周期邊界條件的分數(shù)階脈沖q-差分方程運用Leray-Schauder二擇一定理和Banach壓縮映射原理研究了解的存在性和唯一性.第三章,研究帶有積分邊界條件的二階脈沖微分方程組在非線性項允許變號的情況下,運用了雙錐上的Krasnoselskii不動點定理得到了上述問題兩個非負解的存在性.
[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.
【學位授予單位】：曲阜師范大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O175

【參考文獻】

相關期刊論文 前1條

1 葛渭高;任景莉;;雙錐不動點定理及其在非線性邊值問題中的應用[J];數(shù)學年刊A輯(中文版);2006年02期

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本文編號：1739562