无穷区间上带P-Laplacian算子的分数阶微分方程正解的存在性  

Existence of Positive Solutions for Fractional Differential Equations with p-Laplacian Operator in Infinite Interval

作　　者：刘小刚 王震[1] 惠小健[1] 章培军[1] 任水利[1] LIU Xiao-gang;WANG Zhen;HUI Xiao-jian;ZHANG Pei-jun;REN Shui-li(Department of Science,Xijing University,Xi'an 710123,China)

机构地区：[1]西京学院理学院,陕西西安710123

出　　处：《数学的实践与认识》2021年第13期240-249,共10页Mathematics in Practice and Theory

基　　金：西京学院校科研基金项目(XJ180210);陕西省自然科学基础研究计划青年项目(2021JQ-868);西安市科技计划项目(2019218414GXRC020CG021-GXYD20.3);陕西省教育厅专项科研项目(20JK0965)。

摘　　要：通过修正了一个关于紧性的判别准则,运用Schaefer不动点定理和pLaplace算子Φ_p(s)的特殊性质,将微分系统转化为与其等价的积分系统.借助无穷区间中判别相对紧的方法,在较弱的条件下得到了微分系统解的存在性的充分条件,并且还讨论了无界解的存在性,推广改进了相关研究成果.In this paper,by modifying a criterion about compactness,using Schaefer fixed point theorem and the special properties of P-Laplace operatorΦ_p(s),the differential system is transformed into its equivalent integral system.With the help of the method of judging relative compactness in infinite interval,the sufficient conditions for the existence of solutions of differential systems are obtained under weaker conditions,and the existence of unbounded solutions is also discussed,which generalizes and improves the related research results.

关 键 词：无穷区间 P-LAPLACE算子 分数阶微分方程 正解 

分 类 号：O175[理学—数学]