Electron. J. Differential Equations, Vol. 2023 (2023), No. 30, pp. 1-18.

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

Zhenhai Liu, Nikolaos S. Papageorgiou

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 smooth solutions with sign information and ordered. In the Appendix we develop the spectral properties of the weighted r-Laplace differential operator.

Submitted January 16, 2023. Published March 30, 2023.
Math Subject Classifications: 35J20, 35J60.
Key Words: Constant sign and nodal solutions; nonlinear regularity; nonlinear maximum principle; critical groups; spectrum of weighted r-Laplacian; double resonance.
DOI: https://doi.org/10.58997/ejde.2023.29

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Zhenhai Liu
Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing
Yulin Normal University, Yulin 537000, China
email: zhhliu@hotmail.com
  Nikolaos S. Papageorgiou
Department of Mathematics
National Technical University
Zografou Campus, 15780 Athens, Greece
email: npapg@math.ntua.gr

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