一类带有p-Laplacian算子的分数阶微分方程反周期边值问题解的存在性  

Existence of Solutions for Anti-periodic Boundary Value Problem of Fractional Differential Equations with p-Laplacian Operator

作　　者：贠永震 苏有慧[2] 胡卫敏[1] Yun Yongzhen Su Youhui Hu Weimin(School of Mathematics and Statistic, Yili Normal University, Yining 835000, China School of Mathematics and Physics, Xuzhou Institute of Technology, Xuzhou 221008, China)

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221111

出　　处：《宁夏大学学报（自然科学版）》2017年第1期5-8,14,共5页Journal of Ningxia University(Natural Science Edition)

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(22013-JY-003);徐州工程学院重点项目(2013102)

摘　　要：研究了一类带有p-Laplacian算子的分数阶微分方程反周期边值问题{(Cφp Dα0+u(t))=f(t,u(t)),t∈[0,T],u(0)=-u(T),u′(0)=-u′(T)解的存在性,其中1<α≤2,T>0,φp(s)=s p-1s,p>1,(φp)-1=φq,p-1+q-1=1,CDα0+为Caputo分数阶微分,f:[0,T]×R→R为连续函数.利用分数阶微分方程和反周期边值条件的特性给出所研究边值问题的Green’s函数,然后借助于Banach压缩映像原理和Krasnosel’skiis不动点定理得到此反周期边值问题解的一些新的存在性理论.作为应用,给出了2个例子验证了所得结果.The existence of solutions for the following anti-periodic boundary value problem of fractional differential equations with p-Laplacian operator is concerned.{^Cφp（D0＋^αu（t））=f（t,u（t））,t∈ [0,T],u（0）=-u（T）,u′（0）=-u′（T）,where 1α≤2,T〉0,φp（s）=｜s｜p^-1s,p〉1,（φp）^-1 =φq,p^-1＋q^-1= 1.^CD0＋^αis Caputo fractional derivative andf：[0,T]×R → Ris continuous function.By using the fractional differential equation and anti-periodic boundary value condition,the Green＇s function of the boundary value problem is given,and some new results on the existence of solutions of the fractional boundary value problem are obtained by means of the Banach＇s contraction mapping principle and the Krasnosel＇skiis fixed point theorem.As an application,two examples are presented to illustrate the main results.

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

分 类 号：O175.7[理学—数学]