
Journal of Convex Analysis 28 (2021), No. 3, [final page numbers not yet available] 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. [ Fulltextpdf (145 KB)] for subscribers only. 