Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

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

Mathematics Subject Classification

35J20, 35J60

Suggested citation

Z. Liu, N. S. Papageorgiou. “Nodal Solutions for a Weighted (p,q)-Equation.” Journal of Convex Analysis 29 (2022), No. 2, 559–570.

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