正解论文：两类非线性边值问题正解的存在性和唯一性.doc

正解论文：两类非线性边值问题正解的存在性和唯一性【中文摘要】在第一章中简单介绍了非线性边值问题与非线性算子的研究现状。在第二章中叙述了基本概念和引理。在第三章第一节中利用广义凹与凸算子的不动点定理及格林函数的性质,研究了如下一类非线性四阶两点边值问题：在两种不同的条件下,获得了这类边值问题正解的存在唯一性,推广和完善了文献中的存在性结果。因此,本节结论在边值问题研究方面具有一定的理论意义和参考价值。在第三章第二节中详细研究了如下四阶两点边值问题对称正解的存在性与唯一性：利用不动点指数理论的方法,建立了上述边值问题至少有一个或两个对称正解的结论；进而通过广义-凹算子不动点理论,给出上述边值问题对称正解的存在唯-性的充分性条件。在第四章中研究了如下一类二阶脉冲微分方程Neumann边值问题正解的存在唯一性：所用方法为广义凹算子不动点定理,所获结论和方法在文献并不多见。【英文摘要】In the first chapter,we introduce the development of nonlinear boundary value problem and nonlinear operator theory.In the second chapter,we describe the basic concepts and basic lemmas.In the first section of the third chapter.by using the fixed point theorems of generalized concave and convex operators and the properties of the Green functions,a class of fourth-order boundary value problems is studied as the follow: The existence and uniqueness of positive solutions for this boundary value problem is obtained under two different conditions.The results obtained generalize and com-pliment the related existing ones in references, which has theoretical significance and reference value on boundary value problems.In the second section of the third chapter, the purpose is to investigate the exis-tence and the uniqueness of symmetric positive solutions for the following fourth-order boundary value problem: By using the fixed point index method, we establish the existence of at least one or at least two symmetric positive solutions for the above boundary value problem. Further, by using a fixed point theorem of general-concave operators, we also present criteria which guarantee the existence and uniqueness of symmetric positive solutions for the above boundary value problem.The fourth chapter is concerned with the existence and uniqueness of positive solutions for a class of Neumann boundary value problems of second order impulsive differential equations as the follow:The result is obtained by using a fixed point theorem of generalized concave operators.【备注】索购全文在线加好友：1.3.9.9.3.8848 同时提供论文写作一对一指导和论文发表委托服务。【关键词】正解 对称正解 存在性与唯一性 广义-凹算子不动点定理 四阶两点边值问题 Neumann边值问题【英文关键词】positive solution symmetric positive solution existence and uniqueness fixed point theorem of general-operators fourth-order two-point boundary value problem Neumann boundary value problem【目录】两类非线性边值问题正解的存在性和唯一性中文摘要6-7ABSTRACT7-8第一章 前言9-11第二章 预备知识11-13第三章 四阶两点边值问题正解的存在性和唯一性13-283.1