非线性分数微分方程边值问题正解的存在性与多解性  

Existence and multiplicity of positive solutions to boundary value problem of nonlinear fractional differential equations

作　　者：宋利梅[1] 

机构地区：[1]嘉应学院数学学院,广东梅州514015

出　　处：《兰州理工大学学报》2013年第3期160-163,共4页Journal of Lanzhou University of Technology

基　　金：广东省自然科学基金(10151063101000003);广东省梅州市科学技术局与嘉应学院联合资助项目(2012KJA06)

摘　　要：利用锥上的Krasnosel’skii不动点定理,考察非线性分数微分方程边值问题的正解.结论表明,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).举例说明所得结果的可应用性.Used Krasnosel＇ skii fixed-point theorem on cone, the positive solutions for nonlinear boundary value problem of fractional differential equations were examined. The result showed that the problem would have n positive solutions （n is an arbitrarily given positive integer） provided that the ＂heights＂ of nonlinear term was appropriate on some bounded sets. A example was given to illustrate the applicability of the results obtained.

关 键 词：分数微分方程 边值问题 正解 存在性 多解性 

分 类 号：O175.8[理学—数学]