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Title: On the existence of free vibrations for a beam equation when the period is an irrational multiple of the length (English)
Author: Feireisl, Eduard
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 33
Issue: 2
Year: 1988
Pages: 94-102
Summary lang: English
Summary lang: Russian
Summary lang: Czech
Category: math
Summary: The author examined non-zero $T$-periodic (in time) solutions for a semilinear beam equation under the condition that the period $T$ is an irrational multiple of the length. It is shown that for a.e. $T \in R^1$ (in the sense of the Lebesgue measure on $R^1$) the solutions do exist provided the right-hand side of the equation is sublinear. (English)
Keyword: nonuniqueness
Keyword: time-periodical solutions
Keyword: semilinear equation
Keyword: irrational periods
Keyword: dual variational method
MSC: 35B10
MSC: 35K60
MSC: 35L70
MSC: 58E05
MSC: 73K12
idZBL: Zbl 0684.35057
idMR: MR0940709
DOI: 10.21136/AM.1988.104291
Date available: 2008-05-20T18:34:06Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] J. M. Coron: Periodic solutions of a nonlinear wave equation without assumption of monotonicity.Math. Ann. 262 (1983), 273-285. Zbl 0489.35061, MR 0690201, 10.1007/BF01455317
Reference: [2] D. G. Costa M. Willem: Multiple critical points of invariant functional and applications.Séminaire de Mathématique 2-éme Semestre Université Catholique de Louvain.
Reference: [3] I. Ekeland R. Temam: Convex analysis and variational problems.North-Holland Publishing Company 1976. MR 0463994
Reference: [4] N. Krylová O. Vejvoda: A linear and weakly nonlinear equation of a beam: the boundary value problem for free extremities and its periodic solutions.Czechoslovak Math. J. 21 (1971), 535-566. MR 0289918


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