Least energy solutions with sign information for parametric double phase problems
type: Item
instance of: scholarly article
title: Least energy solutions with sign information for parametric double phase problems
zbMATH Open document ID: 1482.35102
author: Nikolaos S. Papageorgiou
author: Calogero Vetro
author: Francesca Vetro
published in: Results in Mathematics
publication date: 2022-01-31T00:00:00Z
review text: The authors study a parametric double phase Dirichlet problem of the form \begin{align*} \begin{cases} -\Delta_p^q u-\Delta_qu=\lambda|u|^{q-2}u +f(x,u)& \text{in }\Omega,\\ u\big|_{\partial\Omega}=0, \ 1<q<p, \ \lambda\in\mathbb{R}, & \end{cases} \end{align*} where \(a\in L^\infty(\Omega)\) with \(a(z)>0\) for a.\,a.\,\(x\in\Omega\), \(\Delta_p^a\) denotes the weighted \(p\)-Laplace differential operator defined by \begin{align*} \Delta_p^au=\text{div}\left(a(z)|\nabla u|^{p-2}\nabla u\right), \end{align*} while the superlinear perturbation in the reaction satisfies a weak Nehari-type monotonicity. The authors show that the problem has at least three nontrivial solutions all with sign information.
reviewed by: Patrick Winkert
Mathematics Subject Classification ID: 35J92
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35J20
zbMATH DE Number: 7466710
zbMATH Keywords: parametric double phase Dirichlet problem
zbMATH Keywords: existence
zbMATH Keywords: Nehari manifolds
MaRDI profile type: Publication
full work available at URL: s00025-021-01556-6
OpenAlex ID: W4200201617
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DOI: 10.1007/S00025-021-01556-6
description: scientific article; zbMATH DE number 7466710