
Journal of Convex Analysis 28 (2021), No. 3, 967982 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. 