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Journal of Convex Analysis 29 (2022), No. 2, 559--570
Copyright Heldermann Verlag 2022

Nodal Solutions for a Weighted (p,q)-Equation

Zhenhai Liu
Guangxi Colleges and Universities, Key Laboratory of Complex System Optimization, Yulin Normal University, Yulin 537000, P. R. China
and: Key Laboratory of Hybrid Computation and IC Design Analysis,, Guangxi University for Nationalities, Nanning, Guangxi 530006, P. R. China

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

We consider a Dirichlet problem driven by a weighted (p,q)-Laplacian with a reaction that involves a critical term and a locally defined perturbation. Using variational tools and cut-off techniques, we show that the problem has a sequence of arbitrarily small nodal solutions.

Keywords: Weighted (p,q)-Laplacian, critical term, locally defined perturbation, nonlinear regularity, extremal constant sign solutions, nodal solutions, cut-off function.

MSC: 35J20, 35J60.

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