本文選題：脈沖微分方程　切入點(diǎn)：滯后型二階脈沖微分方程　出處：《北京信息科技大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：本文通過運(yùn)用Leggett-Williams不動點(diǎn)定理,不動點(diǎn)指數(shù)理論,特征值理論,變換技巧和H?lder不等式系統(tǒng)地研究了包括二階、四階和n階在內(nèi)的脈沖微分方程邊值問題多個正解的存在性,正解對參數(shù)的連續(xù)依賴性以及正解存在的最優(yōu)區(qū)間。根據(jù)研究內(nèi)容和研究方法,全文共分為五章。第一章緒論,介紹脈沖微分方程邊值問題的研究背景與意義,并根據(jù)國內(nèi)和國外的研究現(xiàn)狀提出了本文所研究的主要內(nèi)容,最后給出本文所需要的一些基本概念和定理。第二章討論了一類帶積分邊界條件的滯后型二階脈沖微分方程邊值問題。首先給出了對應(yīng)的齊次邊值問題的Green函數(shù)的表達(dá)式,并研究了其性質(zhì)。然后利用Leggett-Williams不動點(diǎn)定理和H?lder不等式得到了邊值問題至少存在三個正解的結(jié)果。最后給出了一個相應(yīng)的實(shí)例以說明我們的結(jié)論。第三章研究了一類四階脈沖微分方程邊值問題多個正解的存在性以及對參數(shù)的依賴性。文章通過使用兩個變換和不動點(diǎn)定理,確立脈沖梁方程的正解存在性,多解性和正解對參數(shù)的依賴性。值得一提的是,我們不僅給出了解的范數(shù)估計形式,還討論了解對參數(shù)的依懶性并在最后通過一個實(shí)例驗(yàn)證了主要結(jié)果的正確性。第四章考察了一類n階超前型特征值問題正解的存在性。文章通過使用變換技巧,H?lder不等式以及特征值理論確立了參數(shù)l的最優(yōu)區(qū)間,并且在這個區(qū)間上,我們證明了這個具超前變元的n階脈沖微分方程存在正解。第五章對全篇文章進(jìn)行總結(jié)并展望了今后的研究工作。
[Abstract]:In this paper, Leggett-Williams fixed point theorem, fixed point exponent theory, eigenvalue theory, transformation technique and H? Lder inequality systematically studies the existence of several positive solutions of boundary value problems for impulsive differential equations, including second-order, fourth-order and n-order boundary value problems, the continuous dependence of positive solutions on parameters and the optimal interval of existence of positive solutions. The first chapter introduces the background and significance of the research on boundary value problems of impulsive differential equations, and puts forward the main contents of this paper according to the current research situation both at home and abroad. Finally, some basic concepts and theorems needed in this paper are given. In chapter 2, the boundary value problems of second order impulsive differential equations with integral boundary conditions are discussed. First, the expression of the Green function of the corresponding homogeneous boundary value problem is given. Then by using Leggett-Williams fixed point theorem and H? Lder inequality has obtained that there are at least three positive solutions for boundary value problems. Finally, a corresponding example is given to illustrate our conclusion. In chapter 3, we study the existence of multiple positive solutions for a class of fourth order impulsive differential equation boundary value problems. In this paper, by using two transformations and fixed point theorem, The existence of positive solutions, the multiplicity of solutions and the dependence of positive solutions on parameters of impulsive beam equations are established. Finally, an example is given to verify the correctness of the main results. Chapter 4th investigates the existence of positive solutions for a class of n-order advanced eigenvalue problems. Lder inequality and eigenvalue theory establish the optimal interval of parameter l, and on this interval, We prove the existence of positive solutions for this n-order impulsive differential equation with advanced arguments. Chapter 5th summarizes the whole paper and looks forward to the future research work.
【學(xué)位授予單位】：北京信息科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175.8

【參考文獻(xiàn)】

相關(guān)期刊論文 前2條

1 ;Periodic boundary value problem for the first order functional differential equations with impulses[J];Applied Mathematics:A Journal of Chinese Universities(Series B);2009年01期

2 馬如云;POSITIVE SOLUTIONS OF FOURTH-ORDER TWO-POINT BOUNDARY VALUE PROBLEMS[J];Annals of Differential Equations;1999年03期

，

本文編號：1619558