A weighted (p,2)-equation with double resonance

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;Department of Mathematics National Technical University Zografou Campus

关键词: Constant sign and nodal solutions;    nonlinear regularity;    nonlinear maximum principle;    critical groups;    spectrum of weighted r-Laplacian;    double resonance.;   

DOI  :  10.58997/ejde.2023.29

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

We consider a Dirichlet problem driven by a weighted (p,2)-Laplacian with a reaction which is resonant both at\(\pm\infty\)and at zero(double resonance). We prove a multiplicity theorem producing three nontivial smoothsolutions with sign information and ordered.In the Appendix we develop the spectral properties of the weighted r-Laplace differential operator.

【 授权许可】

CC BY