一类非线性项带导数的p-Laplacian边值问题正解的存在性和多解性  

Existence and Multiplicity of Positive Solutions for a Class of Nonlinear p-Laplacian Boundary Value Problems with Derivatives

作　　者：苏有慧[1] 孙文超 孙爱 SU Youhui;SUN Wenchao;SUN Ai(School of Mathematics and Physics,Xuzhou University of Technology,Xuzhou 221018,China)

机构地区：[1]徐州工程学院数学与统计学院,徐州221018

出　　处：《应用数学学报》2023年第2期261-276,共16页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(批准号:12126427,12161079)资助项目。

摘　　要：本文研究了一类非线性项带导数的p-Laplacian算子的分数阶微分方程边值问题正解的存在性和多解性.首先,利用分数阶微分方程和边值条件给出了该边值问题的Green函数,然后利用Guo-Krasnosel’skii’s不动点定理和Leggett-Williams不动点定理得出该边值问题一个或者三个正解的存在性结论.作为应用,给出两个例子验证了结论的适用性,特别是,用迭代法进行了逼近模拟,给出解的图形.值得一提的是此文研究的微分方程的非线性项是带有Riemann-Liouville型分数阶微分.In this paper,the existence and multiplicity of positive solutions to a class of p-Laplacian fractional differential equations whose nonlinearity contains the derivative explicitly is considered.First,the Green function of the boundary value problem is given by using fractional differential equations and boundary value conditions,and then the existence of one or three positive solutions to the boundary value problem are obtained by the Guo-Krasnosel'skii's fixed point theorem and Leggett-Williams fixed point theorem.As applications,two examples are given to verify the applicability of the conclusion,in particular,the solution of the graphics are given by using the iterative method and simulation approximate approach.It is worth mentioned that the nonlinear term of the differential equation which is studied in this paper involves the Riemann-Liouville fractional differentiation.

关 键 词：分数阶微分方程 P-LAPLACIAN算子 边值问题 不动点定理 

分 类 号：O175.8[理学—数学]