非合作的分数阶耦合系统的正解  

The Existence of Solution of Non-cooperative Fractional Coupled Systems

作　　者：李素红[1] 李丽华[1] 武利猛[1] LI Suhong;LI Lihua;WU Limeng(School of Mathematics and Information Science&Technology,Hebei Normal University of Science&technology,Qinhuangdao Hebei,066004,China)

机构地区：[1]河北科技师范学院数学与信息科技学院

出　　处：《河北科技师范学院学报》2019年第4期52-59,78,共9页Journal of Hebei Normal University of Science & Technology

摘　　要：对非合作的分数阶耦合系统D^p1[x(t)]=g 1(t,y(t),D^α1 y(t))D^ p 2[y(t)]=g 2(t,x(t),D^α2 x(t))其中1<p 1,p 2<2,α1,α2>0,p 1-α2≥1,p 2-α1≥1,通过设置合适的工作空间,并赋予适当的范数,构造乘积锥,运用锥上的不动点定理探讨了当非线性项g 1,g 2:[0,1]×R×R→R超线性或次线性增长时,该系统正解的存在性。结果表明,该系统至少存在一组正解。通过一个具体实例阐明了本次研究得到的结果。In this paper,the following non-cooperative fractional coupling system is analyzed D ^P 1[x(t)]=g 1(t,y(t),D^α1 y(t))D ^P 2[y(t)]=g 2(t,x(t),D^α2 x(t))where 1<p 1,p 2<2,α1,α2>0,p 1-α2≥1,p 2-α1≥1.By setting suitable working spaces and giving proper norms,the product cone is constructed,and the fixed point theorem on the cone is used to explore the existence of the positive solutions to the system when the nonlinearites satisfy some conditions.Finally,the results of this paper are illustrated by a specific example.

关 键 词：耦合系统 锥上不动点定理 分数阶导数 正解 增长条件 

分 类 号：O175.29[理学—数学]