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Sbornik: Mathematics, 1998, Volume 189, Issue 3, Pages 383–397
DOI: https://doi.org/10.1070/sm1998v189n03ABEH000307 (Mi sm307) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Parametric oscillations of a singularly perturbed telegraph equation with a pendulum non-linearity

Yu. S. Kolesov

P. G. Demidov Yaroslavl State University
English version PDF (193 kB) Citations (3)
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DOI: https://doi.org/10.1070/sm1998v189n03ABEH000307
Abstract: The solution of the problem in the title is reduced to an analysis of the question of the number of and stability of equilibrium states of the quasi-normal form of the boundary-value problem under consideration. A mechanism is revealed for the origin of its so-called simple equilibrium states. It is shown that as the coefficient of elasticity decreases, the number of such states increases, and that those of them with the most complex spatial structure are stable.
Received: 21.03.1997
Russian version:
Matematicheskii Sbornik, 1998, Volume 189, Number 3, Pages 69–82
DOI: https://doi.org/10.4213/sm307
Bibliographic databases:
UDC: 517.926
MSC: Primary 35L70, 35B25; Secondary 35L05, 34B15, 34D15
Language: English
Original paper language: Russian
Citation: Yu. S. Kolesov, “Parametric oscillations of a singularly perturbed telegraph equation with a pendulum non-linearity”, Mat. Sb., 189:3 (1998), 69–82; Sb. Math., 189:3 (1998), 383–397
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    English version PDF:13
    References:41
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