一类分数阶p-Laplacian具积分边界的多点边值问题  

Existence of Solutions for a Class of Integral and Multi-Point Boundary Value Problem with P-Laplacian Operators

作　　者：王和香 WANG He-xiang(School of Mathematics and Statistic,Kashgar University,Kashgar 844006,China)

机构地区：[1]喀什大学数学与统计学院

出　　处：《数学的实践与认识》2018年第23期264-271,共8页Mathematics in Practice and Theory

基　　金：喀什大学校内课题((16)2588)

摘　　要：在含p-laplacian算子的基础上,将多点边界条件与积分边界条件相结合,研究一类新的任意阶分数微分方程.通过求解等价积分方程,得到格林函数,再定义一个Banach空间中的连续算子,最后利用锥理论和不动点定理证明边值问题解的存在性,并通过实例验证所得结果的有效性。Based on the p-Laplacian operator,this paper concerns a r/ew kind of fractional differential equation of arbitrary order by combining a multi-point boundary conditiof/with an integral boundary condition.By solving the equation which is equivalent to the problem we are going to investigate,the Green's functions are obtained.By defining a continuous operator on a Banach space and taking advantage of thecone theory and some fixed point theorems,obtain the existence of solutions for the BVPs.The last,we will examine the efficiency for the results via examples.

关 键 词：分数阶边值问题 P-LAPLACIAN算子 积分边界条件 多点边界条件 

分 类 号：O175.8[理学—数学]