一类非线性分数阶微分方程边值问题正解的存在性

基金项目:

广东省自然科学基金资助项目;广东省梅州市科学技术局与嘉应学院联合资助项目

详细信息

Existence of positive solutions to boundary value problem for a nonlinearfractional differential equations

摘要: 研究了一类非线性分数阶微分方程边值问题正解的存在性. 主要方法是锥内的 Krasnosel'skii 不动点定理的应用.结果表明: 只要非线性项在某些有界集合上的 "高度" 是适当的, 该问题有n个正解 (n是一个任意给定的正整数).
- 分数阶微分方程 /
- 边值问题 /
- 正解 /
- 存在性
Abstract: The existence of positive solutions to a boundary value problem for a nonlinear fractional differential equation is investigated. The main method is a local application of Krasnosel'skii fixed-point theorem of cone expansion-compression type. The main results show that the boundary value problem has at least $n$ positive solutions provided that the "height" is appropriate on some bounded sets ( $n$ is a positive integer number arbitrarily given )
- fractional differential equation /
- boundary value problems /
- positive solutions /
- exitence