Journal of Convex Analysis 28 (2021), No. 3, 967--982
Copyright Heldermann Verlag 2021
Superlinear Weighted (p,q)-Equations with Indefinite Potential
Zhenhai Liu
Guangxi Colleges, Yulin Normal University, Yulin, P. R. China
and: Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi University for Nationalities, Nanning, Guangxi, P. R. China
zhhliu@hotmail.com
Nikolaos S. Papageorgiou
Department of Mathematics, National Technical University, 15780 Athens, Greece
npapg@math.ntua.gr
We consider a nonlinear Dirichlet problem driven by a weighted $(p,q)$-Laplacian plus an indefinite potential term. The reaction is superlinear. We prove a three solutions theorem providing sign information for all of them (positive, negative, nodal). The nodal solution is produced using flow invariance arguments.
Keywords: Weighted (p,q)-Laplacian, nonlinear maximum principle, extremal constant sign solutions, nodal solution, indefinite potential.
MSC: 35J20, 35J60.
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