Positive Solutions for Resonant (p, q)-equations with convection

Advances in Nonlinear Analysis

Papageorgiou Nikolaos S.¹  Liu Zhenhai² 

[1] Department of Mathematics, National Technical University, Zografou Campus, 15780Athens, Greece;Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin537000, P.R. China;

关键词: singular term;    resonance;    nonlinear regularity;    leray-schauder alternative principle;    minimal solution;    iterative asymptotic process;    35j60;    35j91;    35j92;    35d30;    35d35;   

DOI  :  10.1515/anona-2020-0108

来源: DOAJ

【 摘 要 】

We consider a nonlinear parametric Dirichlet problem driven by the (p, q)-Laplacian (double phase problem) with a reaction exhibiting the competing effects of three different terms. A parametric one consisting of the sum of a singular term and of a drift term (convection) and of a nonparametric perturbation which is resonant. Using the frozen variable method and eventually a fixed point argument based on an iterative asymptotic process, we show that the problem has a positive smooth solution.

【 授权许可】

Unknown