Zhenhai Liu, Nikolaos S. Papageorgiou
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 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 |
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| Nikolaos S. Papageorgiou Department of Mathematics National Technical University Zografou Campus, 15780 Athens, Greece email: npapg@math.ntua.gr |
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