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
zhhliu@hotmail.com
Nikolaos S. Papageorgiou
Department of Mathematics, National Technical University, Athens, Greece
npapg@math.ntua.gr
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.
[ Fulltext-pdf (119 KB)] for subscribers only.