The existence of nontrivial solutions to a class of quasilinear equations
type: Item
instance of: scholarly article
title: The existence of nontrivial solutions to a class of quasilinear equations
zbMATH Open document ID: 1466.35191
DOI: 10.1155/2021/9986047
author: Xiaoyao Jia
author: Zhenluo Lou
published in: Journal of Function Spaces
publication date: 2021-06-04T00:00:00Z
review text: Summary: In this paper, we study the following quasilinear equation: \(-\operatorname{div}(\phi (|\nabla u|) \nabla u)+\phi (|u|)u=f(u)\text{ in } \mathbb{R}^N\), where \(\phi\in C^1(\mathbb{R}^+ , \mathbb{R}^+)\) and \(\Phi (t)= \int_0^ts\phi (|s|)ds\). In the Orlicz-Sobolev space, by variational methods and a minimax theorem, we prove the equation has a nontrivial solution.
Mathematics Subject Classification ID: 35J62
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35A15
zbMATH DE Number: 7355404
zbMATH Keywords: quasilinear equations
zbMATH Keywords: existence of solutions
zbMATH Keywords: variational methods
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/9986047
OpenAlex ID: W3158950822
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description: scientific article; zbMATH DE number 7355404