一类Caputo分数阶p-Laplace反周期边值问题解的存在性  

Existence of solutions to anti-periodic Caputo fractional boundary value problem with p-Laplacian operator

作　　者：贠永震 苏有慧[2] 胡卫敏[1] 

机构地区：[1]伊犁师范学院数学与统计学院,新疆伊宁835000 [2]徐州工程学院数学与物理科学学院,江苏徐州221018

出　　处：《西北师范大学学报（自然科学版）》2017年第3期13-18,共6页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11361047;11501560);江苏省自然科学基金资助项目(BK20151160);青海省自然科学基金资助项目(2012-Z-910);江苏省六大人才高峰项目(2013-JY-003);徐州工程学院重点项目(2013102)

摘　　要：研究一类带有p-Laplace算子的Caputo分数阶微分方程反周期边值问题解的存在性.首先给出了所研究的分数阶边值问题的Green函数,并将研究Caputo分数阶p-Laplace微分边值问题解的存在性问题转化为研究一个非线性算子的不动点问题,然后利用Banach压缩映像原理和Schauder不动点定理得到边值问题解的存在性,最后,通过一个例子验证了本文的主要结果.The existence of solutions to anti-periodic Caputo fractional boundary value problem withp-Laplacian operator is investigated in this paper. The green function of the anti-periodic Caputo fractionalboundary value problem is given, and it is proved that finding the solutions to the problem is equivalent tofinding the fixed points of the associated functional. Then, by means of the Banach＇s contraction mappingprinciple and Schauder fixed point theorem, some existence results are obtained. Finally, an example isprovided for illustrating the application of our main results.

关 键 词：Caputo分数阶微分方程 反周期边值问题 解的存在性 P-LAPLACE算子 

分 类 号：O175.8[理学—数学]