Dirichlet (p,q)-equations with gradient dependent and locally defined reaction

Electronic Journal of Differential Equations

article

Zhenhai Liu¹  Nikolaos S. Papageorgiou² 

[1] Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal University Yulin 537000;Department of Mathematics National Technical University Zografou Campus

关键词: (p;    q)-differential operator;    convection;    fixed point;    nonlinear;    regularity;    positive solution;    Leray-Schauder alternative theorem.;   

DOI  :  10.58997/ejde.2021.34

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

We consider a Dirichlet (p,q)-equation, with a gradient dependent reaction which is onlylocally defined. Using truncations, theory of nonlinear operators of monotone type,and fixed point theory (the Leray-Schauder Alternative Theorem), we show the existenceof a positive smooth solution.

【 授权许可】

CC BY