Multiple solutions for \((p, 2)\)-equations at resonance
type: Item
instance of: scholarly article
title: Multiple solutions for \((p, 2)\)-equations at resonance
zbMATH Open document ID: 1421.35177
author: Nikolaos S. Papageorgiou
author: Calogero Vetro
author: Francesca Vetro
published in: Discrete and Continuous Dynamical Systems. Series S
publication date: 2019-03-27T00:00:00Z
review text: The authors study a nonlinear nonhomogeneous Dirichlet problem with a $(p,2)$-Laplacian and a reaction term $(p-1)$-linear and resonant with respect to any nonprincipal variational eigenvalue of the minus $p$-Laplacian. The main existence result provides six solutions (five of them with precise sign and order information). The first four solutions are obtained as minima of the energy functionals corresponding to appropriate truncations of the reaction term. The fifth, sign-changing, solution is obtained between the largest negative and the smallest positive ones. The last solution is provided by Morse theory.
reviewed by: Leszek Gasiński
Mathematics Subject Classification ID: 35J92
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 7043511
zbMATH Keywords: \((p,2)\)-Laplacian
zbMATH Keywords: nonhomogeneous Dirichlet problem
zbMATH Keywords: existence of solutions
MaRDI profile type: Publication
full work available at URL: dcdss.2019024
OpenAlex ID: W2887381716
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DOI: 10.3934/DCDSS.2019024
description: scientific article; zbMATH DE number 7043511