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:

03736725 
Volume:

33 
Issue:

2 
Year:

1988 
Pages:

94102 
Summary lang:

English 
Summary lang:

Russian 
Summary lang:

Czech 
. 
Category:

math 
. 
Summary:

The author examined nonzero $T$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 righthand side of the equation is sublinear. (English) 
Keyword:

nonuniqueness 
Keyword:

timeperiodical 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:

20080520T18:34:06Z 
Last updated:

20200728 
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), 273285. 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 2éme Semestre Université Catholique de Louvain. 
Reference:

[3] I. Ekeland R. Temam: Convex analysis and variational problems.NorthHolland 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), 535566. MR 0289918 
. 