Periodic solutions of some semilinear wave equations on balls and on spheres
type: Item
instance of: scholarly article
title: Periodic solutions of some semilinear wave equations on balls and on spheres
zbMATH Open document ID: 0790.35070
DOI: 10.12775/TMNA.1993.010
author: V. Pereyra
published in: Topological Methods in Nonlinear Analysis
publication date: 1994-01-06T00:00:00Z
review text: Radially symmetric solutions of the problem \[ u_{tt}- \Delta u+ g(u)= f(t,x), \qquad (t,x)\in \mathbb{R}\times B_ a^ n, \] \[ u(t,x)=0, \quad (t,x)\in\mathbb{R} \times S_ a^{n-1}, \qquad u(t+T,x)= u(t,x), \quad (t,x)\in \mathbb{R}\times B_ a^ n \] are considered where \(S_ a^{n-1}= \{x\in\mathbb{R}^ n\): \(\| x\|=a\}\), \(B_ a^ n= \{x\in \mathbb{R}^ n\): \(\| x\|<a\}\). In the case of even \(n\) it is supposed that \(g(t,x,u)\) satisfies nonresonance conditions of non-uniform type with respect to \(t\) and \(x\). In the case of odd \(n\) using recent existence theorems of the authors, a result of Smiley is improved by providing sharp conditions on the monotonicity constants of \(g(t,x,u)\) which insure the existence and uniqueness of the solution.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 35L20
zbMATH DE Number: 482110
zbMATH Keywords: semilinear wave equations on balls and on spheres
zbMATH Keywords: radially symmetric solutions
zbMATH Keywords: nonresonance conditions
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
reviewed by: Stepan Agop Tersian
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 482110