分数阶微分方程边值问题正解的局部存在与多解性  

Local Existence and Multiulicity of Positive Solutions to Boundary Value Problem for A 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：《嘉应学院学报》2012年第8期13-18,共6页Journal of Jiaying University

基　　金：广东省自然科学基金资助项目(10151063101000003);梅州市科学技术局与嘉应学院联合资助项目(2010KJA34)

摘　　要：应用Green函数将分数微分方程边值问题转化为积分方程的方法讨论分数阶微分方程边值问题正解的存在性.研究非线性分数阶微分方程的两点边值问题,主要工具是锥上的Krasnosel'skii不动点定理.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).By means of the Green’s function,the boundary value problem of fractional differential equation can be reduced to the equivalent internal equation.This method is used successfully to discuss the existence of the positive solution to boundary value problem of nonlinear fractional differential equation.This article investigates the two-point boundary value problem to a nonlinear fractional differential equations.Main results show that the problem has at least positive solutions drovided that the ＂heights＂ of the nonlinear term is appropriate on some bounded sets（n is a positive intr number arbitrary given）.The main ingredient is Krasnosel’skii fixed-point theorem on cone.

关 键 词：分数阶微分方程 边值问题 正解 存在性 多解性 

分 类 号：O175.8[理学—数学]