\((p, q)\)-Laplacian problems with parameters in bounded and unbounded domains
type: Item
instance of: scholarly article
title: \((p, q)\)-Laplacian problems with parameters in bounded and unbounded domains
zbMATH Open document ID: 1547.35384
author: Said El Manouni
author: Kanishka Perera
author: Patrick Winkert
published in: Houston Journal of Mathematics
publication date: 2024-08-19T00:00:00Z
review text: This article is concerned with the existence and nonexistence of positive solutions for differential equations of the type \(-\Delta_p u-\Delta_q u=\lambda f(x,u)+\mu g(x, u)\) in bounded and unbounded domains. The nonlinearities \(f\) and \(g\) satisfy some growth conditions such as \(|f(x,u)|\leq C|u|^{p-1}\), \(|g(x,u)|\leq Cu^{q-1}\). Under some extra conditions involving \(\lambda\) and \(\mu\), the authors derive estiatence and nonexistence of positiove solutions. The approach is variational and relies on critical point theorems with Pale-Smale condition.
reviewed by: Marius Ghergu
Mathematics Subject Classification ID: 35J92
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35A15
zbMATH DE Number: 7898655
zbMATH Keywords: \((p, q)\)-Laplacian
zbMATH Keywords: existence and nonexistence of positive solutions
zbMATH Keywords: variational approach
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7898655