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

【摘要】：非線(xiàn)性泛函分析作為數(shù)學(xué)中一個(gè)既有深刻理論又有廣泛應(yīng)用的研究領(lǐng)域,它以自然界中出現(xiàn)的非線(xiàn)性問(wèn)題為背景,建立了處理非線(xiàn)性問(wèn)題的若干一般性理論和方法.近年來(lái),非線(xiàn)性微分方程已經(jīng)引起國(guó)內(nèi)外數(shù)學(xué)界及自然科學(xué)界的高度重視,成為國(guó)際研究熱點(diǎn)方向之一.脈沖微分方程在化學(xué)、工程、種群動(dòng)態(tài)和經(jīng)濟(jì)學(xué)等諸多領(lǐng)域得到以廣泛應(yīng)用.許多數(shù)學(xué)家應(yīng)用非線(xiàn)性分析工具得到了非線(xiàn)性脈沖微分方程解的存在性和解的性質(zhì)等結(jié)論.本文主要研究幾類(lèi)非線(xiàn)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?jǐn)?shù)階脈沖積分-微分方程反周期邊值問(wèn)題運(yùn)用Banach壓縮映射原理和Krasnoselskii不動(dòng)點(diǎn)定理,得到上述問(wèn)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?jǐn)?shù)階脈沖q-差分方程運(yùn)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(xiàn)性項(xiàng)允許變號(hào)的情況下,運(yùn)用了雙錐上的Krasnoselskii不動(dòng)點(diǎn)定理得到了上述問(wèn)題兩個(gè)非負(fù)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(xué)位授予單位】：曲阜師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O175

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 葛渭高;任景莉;;雙錐不動(dòng)點(diǎn)定理及其在非線(xiàn)性邊值問(wèn)題中的應(yīng)用[J];數(shù)學(xué)年刊A輯(中文版);2006年02期

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本文編號(hào)：1739562