Solutions of minimal period for a semilinear wave equation
type: Item
instance of: scholarly article
title: Solutions of minimal period for a semilinear wave equation
zbMATH Open document ID: 0714.35052
DOI: 10.1007/BF01765945
author: Addolorata Salvatore
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1989-01-01T00:00:00Z
review text: The paper is dedicated to existence of time-periodic solutions u(x,t) of the boundary value problem for a semilinear wave equation containing only the nonlinearity g(u). The solutions in question are of prescribed minimal period T. The main results are given in the form of the two basic existence theorems. The sufficient conditions of those include some restrictions on monotonicity, smoothness and growth of the function g(u). The proofs of the theorems use the generalized Morse index of a solution and the dual variational methods in a critical point theory. References, 22 in number, fully cover the stated problem.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 4175568
zbMATH Keywords: semilinear wave equation
zbMATH Keywords: minimal period
zbMATH Keywords: existence
zbMATH Keywords: Morse index
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01765945
OpenAlex ID: W4243436097
description: scientific article; zbMATH DE number 4175568