一类三阶非线性微分方程两点边值问题的变号解
Sign-Changing Solutions for Two-Point Boundary Value Problems of Three-Order Nonlinear Differential Equations
DOI: 10.12677/AAM.2017.68116, PDF, HTML, XML, 下载: 1,559  浏览: 2,770  科研立项经费支持
作者: 纪宏伟：南通师范高等专科学校数理系，江苏 南通
关键词: 格结构；三阶两点边值问题；变号解；Lattice Structure； Third-Order Two-Point Boundary Value Problem； Sign-Changing Solutions
摘要: 利用Banach格与拓扑度相结合的理论讨论带有边值的三阶微分方程两点边值问题，其中，得到所述问题变号解的存在性结果。进一步，如果f是奇函数，则问题有两个变号解。
Abstract: In this paper, we use the fixed point theorem with Banach lattice structure and topological degree to discuss the three-order two-point boundary value problem for all subject to , where  . If f satisfies certain conditions, then the existence result of the sign-changing solution is obtained. Moreover, if   is odd for all  , then the problem has two sign-changing solutions.
文章引用：纪宏伟. 一类三阶非线性微分方程两点边值问题的变号解[J]. 应用数学进展, 2017, 6(8): 968-974. https://doi.org/10.12677/AAM.2017.68116

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