# Article

 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: http://hdl.handle.net/10338.dmlcz/104291 . 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 .

## Files

Files Size Format View
AplMat_33-1988-2_2.pdf 977.3Kb application/pdf View/Open

Partner of