理论数学  >> Vol. 3 No. 6 (November 2013)

一类四阶两点边值问题正解的存在性与多解性
Existence and Multiplicity of Positive Solutions for a Fourth-Order Two-Point Boundary Value Problem

DOI: 10.12677/PM.2013.36053, PDF,  被引量 下载: 2,435  浏览: 5,764  国家自然科学基金支持

作者: 余 立:南京航空航天大学理学院,南京

关键词: 两点边值问题正解上下解方法拓扑度Two-Point Boundary Problem; Positive Solutions; Lower and Upper Solutions; Topological Degree

摘要: 本文讨论非线性四阶两点边值问题。正解的存在性与多解性,其中为参数。运用上下解方法和拓扑度理论,在非线性项满足较弱条件时,获得了上述问题正解及多个正解的存在性。
Abstract: In this paper, using the lower and upper solution methods and the topological degree theory, we study the fourth-order two-point boundary value problem , , ,with nonhomogeneous boundary condition, where >0 is a parameter,. Under a weaker condition on ƒ , we obtain the exis- tence of a positive solution and multiple positive solutions for this class of problems.

文章引用: 余立. 一类四阶两点边值问题正解的存在性与多解性[J]. 理论数学, 2013, 3(6): 347-353. http://dx.doi.org/10.12677/PM.2013.36053

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