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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

Nikolaos S. Papageorgiou
Department of Mathematics, National Technical University, 15780 Athens, Greece

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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