一类具有p-Laplacian算子的奇异分数阶微分方程无穷点边值问题的正解  

Positive Solutions for Some Singular Fractional Differential Equation Infinite p-point Boundary Value Problems with-Laplacian

作　　者：仲秋艳[1] 张兴秋[2] 

机构地区：[1]济宁医学院信息技术中心,山东济宁272067 [2]济宁医学院医学信息工程学院,山东日照276826

出　　处：《聊城大学学报（自然科学版）》2016年第2期25-32,共8页Journal of Liaocheng University:Natural Science Edition

基　　金：国家自然科学基金(11371221;11071141);济宁医学院科技计划(JY2015KJ019);山东省高校科技发展计划(J15LI16);山东省自然科学基金(ZR2015AL002)资助

摘　　要：研究一类具有p-Laplacian算子的非线性奇异分数阶微分方程无穷点边值问题的正解.非线性项允许关于时间和空间变量具有奇异性.通过对Green函数的性质进行进一步研究,构造出特殊的锥,引入适当的高度函数并考虑高度函数在锥中某些有界集合上的积分,给出了所研究问题局部正解以及多个局部正解的存在性结果.Existence of positive solutions for some nonlinear fractional differential equation infinitepointboundary value problems with ^-Laplacian is considered in this paper. The nonlinear term f permitssingularities with respect to both the time and space variables. A special cone is constructed by furtherinvestigating the properties of Green function. By introducing height functions of the nonlinear termon some bounded sets and considering integrations of these height functions, several local existence andmultiplicity of positive solutions theorems are obtained.

关 键 词：分数阶微分方程 P-LAPLACIAN 无穷点边值 高度函数 奇异 

分 类 号：O175.8[理学—数学]