On the existence and nonexistence of periodic solutions to some nonlinear hyperbolic equations
type: Item
instance of: scholarly article
title: On the existence and nonexistence of periodic solutions to some nonlinear hyperbolic equations
zbMATH Open document ID: 0972.35073
published in: Doklady Mathematics
publication date: 2001-01-28T00:00:00Z
review text: The author considers multidimensional hyperbolic equations with nonlinear principal part. For a class of nonlinear hyperbolic equations with homogeneous terms the method of separation of variables and variational approach is used to prove the existence of periodic solutions. The proof of the nonexistence of nontrivial periodic solutions is based on new hyperbolic variational identities. The results are represented without proofs which will be published elsewhere.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B10
zbMATH DE Number: 1557540
zbMATH Keywords: separation of variables
zbMATH Keywords: variational approach
zbMATH Keywords: new hyperbolic variational identities
author: S. I. Pokhozhaev
reviewed by: Vesa Mustonen
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1557540