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Journal of Mathematical Analysis and Applications
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Journal of Mathematical Analysis and Applications
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On Bounded and Time-Periodic Solutions of Nonlinear Wave Equations

On bounded and time-periodic solutions of nonlinear wave equations
descriptionPublicationkeyboard_double_arrow_right Article 01 Jul 2001 English Publisher:Elsevier BVJournal:Journal of Mathematical Analysis and Applications, volume 259, pages 253-276 (issn: 0022-247X, Copyright policy )
Authors: Kiguradze, Tariel;

doi: 10.1006/jmaa.2000.7500

On Bounded and Time-Periodic Solutions of Nonlinear Wave Equations

Abstract

A nonlinear wave equation of the form: \[ u_{tt} - u_{ss} = g(t,s,u) + g_1(u) u_t \] on an infinite strip \(\mathbb{R} \times [0,a]\) is studied. Suffient conditions are given in terms of the structural properties of the functions \(g\) and \(g_1\) for the problem to possess at least one time-periodic solution provided \(g\) is periodic in \(t\). Uniqueness of these solutions is also studied.

Related Organizations
Keywords

at least one time-periodic solution, Applied Mathematics, uniqueness, Analysis, Periodic solutions to PDEs, Second-order nonlinear hyperbolic equations

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
10
Top 10%
Top 10%
Average
hybrid