A system of wave inequalities with inverse-square potentials in an exterior domain
type: Item
instance of: scholarly article
title: A system of wave inequalities with inverse-square potentials in an exterior domain
DOI: 10.1080/00036811.2023.2210154
author: Areej Bin Sultan
author: Mohamed Jleli
author: Bessem Samet
published in: Applicable Analysis
publication date: 2024-09-19T00:00:00Z
review text: This article is concerned with the existence and nonexistence of solutions to the coupled wave inequalities \(u_{tt}-\Delta u+\frac{\lambda}{|x|^2}u\geq |x|^a |v|^p\) for \((t, x)\in (0, \infty)\times B_1^c\) and \(v_{tt}-\Delta v+\frac{\lambda}{|x|^2}v\geq |x|^b |u|^q\) for \((t, x)\in (0, \infty)\times B_1^c\). Here \(B_1^c\) denotes the complement of the open unit ball in \(\mathbb{R}^N\), \(N\geq 2\), \(p, q>1\) and \(\lambda\geq - (N-2)^2/4\). Also, it is assumed that \((u, v)\) satisfies \(u\geq f\) and \(v\geq g\) on \((0,\infty)\times \partial B_1\). The two main results of the article provide necessary and suffient conditions for existence and nonexistence of solutions. Some particular cases are also included in the analysis. The approach is technical and relies on various integral estimates. One particular point to note is the careful selection of test functions in order to derive the nonexistence of a solution.
reviewed by: Marius Ghergu
Mathematics Subject Classification ID: 35R45
Mathematics Subject Classification ID: 35L53
Mathematics Subject Classification ID: 35L71
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 35B44
zbMATH DE Number: 7915841
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7915841