【作者】 洪子康；

【导师】 夏大峰；

【作者基本信息】 南京信息工程大学 ， 应用数学， 2011， 硕士

【摘要】 本文主要研究了一类二阶微分方程组边值问题和一类奇异p-Laplacian方程及n维p-Laplacian方程组边值问题正解的存在性.本文共分为四章：第一章,简述了问题产生的历史背景和现阶段的主要成果,并概述本文的主要工作.第二章,主要运用Krasnosel’skii不动点定理,研究了二阶微分方程组边值问题在某些条件下一个正解的存在性.第三章,主要运用Leggett-Williams定理研究了一类形如的奇异p-Laplacian方程边值问题,给出了在一定条件下具有三个解的充分条件.第四章,利用不动点指数理论,建立了n维p-Laplacian方程组三点奇异边值问题一解、两解的存在定理.更多还原

【Abstract】 This paper mainly researches on the existence of positive solutions of boundary value problems for a kind of second order differential equations and singular p-Laplacian equation and n-dimension p-Laplacian equations. This article is divided into four chapters:The first chapter outlines the problem of the historical background and the main results of the present stage, outlines the main work of this paper.ChapterⅡ, by using Krasnosel’skii fixed point theorem, it mainly researches on the existence of one positive solution of boundary value problems for second order differential equations.ChapterⅢ, by using Leggett-Williams theorem, it mainly researches on the existence of three positive solutions for boundary value problem of one kind of p-Laplacian equation and also give the sufficient conditions of the existence of three positive solutions.Chapter IV, by using fixed point index theorem, it mainly establishes the existence theorem of one positive solution and two positive solutions of three-point singular boundary value problems for n-dimensional p-Laplacian.更多还原