Almost-periodic solutions of a class of linear hyperbolic equations
type: Item
instance of: scholarly article
title: Almost-periodic solutions of a class of linear hyperbolic equations
zbMATH Open document ID: 0839.35005
DOI: 10.1007/BF02110749
author: S. V. Zelik
published in: Mathematical Notes
publication date: 1996-06-19T00:00:00Z
review text: S. L. Sobolev proved in 1945 that all solutions of the problem \(u_{tt}(x, t)+ (- \Delta + q(x)) u(x, t)= 0\), \(u|_{\partial\Omega}= 0\), where \(\Omega\subset \mathbb{R}^n\) is a bounded region, \(q(x)\geq 0\), \(x\in \Omega\), \(u|_{t= 0}\in H_1(\Omega)\), \(u_t|_{t= 0}\in L_2(\Omega)\), belong to the class of almost periodic functions with values in the energy field. In this paper the operator \(-\Delta+ q(x)\) is replaced by an abstract selfadjoint operator \(A\) in the Hilbert space and the problem of almost periodic solutions of the corresponding equation is considered.
Mathematics Subject Classification ID: 35B15
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 34G10
zbMATH DE Number: 830717
zbMATH Keywords: nonresonance condition
MaRDI profile type: Publication
cites work: Q3049314
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description: scientific article; zbMATH DE number 830717