Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 30, pp. 1-18.

Title: A weighted (p,2)-equation with double resonance
       
Authors: Zhenhai Liu (Yulin Normal Univ., Yulin 537000,  China)
         Nikolaos S. Papageorgiou (National Technical Univ., Zografou Campus, Athens, Greece)

Abstract:
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 nontrivial  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.