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具p-Laplacian算子型多点边值问题正解存在性
Positive Solutions to Multi-point Boundary Value Problems with P-Laplacian Operator
【作者】 王礼胜；
【导师】 刘斌；
【作者基本信息】 华中科技大学 ， 应用数学， 2007， 硕士
【摘要】 非线性微分方程的奇异边值问题是微分方程中一个非常重要的研究领域,它出现在各种应用学科中,例如核物理、气体动力学、流体力学、边界层理论、非线性光学等。关于奇异p-Laplacian非线性边值间题正解存在性的研究日益受到人们的重视,所用到的方法有拓扑度理论、Schaude不动点定理、上下解方法、打靶法等。本文主要研究具有变号非线性项的两点、三点边值问题正解的存在性以及具p-Laplacian算子型方程组正解的存在性。全文共分三章,主要内容如下:第一章绪论介绍有关边值间题的正解的发展概况,并概述了本文的主要工作。第二章研究依赖于一阶导数的两点及三点边值问题正解的存在性。第三章研究具p-Laplacian算子型方程组多个正解的存在性。
【Abstract】 The singular boundary value problem of nonlinear diferential equations is an important research field in diferential equations, which arises in all sorts of applied branch of learning, such as nuclear physics、gas dynamics、fluid mechanics、theory of boundary layer、nonlinear optics and so on. The research on the existence of positive solutions for singular p-Laplacian boundary value problems has brought people’s attention and those results have been obtained by using topological degree theory、Schauder fixed point theorem、upper-lower solutions method and shooting method and so on.In chapter one, we introduce a survey to the development of positive boundary value problems. We also summarize main results in the dissertation.In chapter two, we discuss the existence of positive solutions for two-point and three-point boundary value problems with the nonlinearity depending on the first order derivative.In chapter three, we discuss the multiplicity results of positive solutions for three-point boundary value systems with p-Laplacian.