# On the existence of free vibrations for a beam equation when the period is an irrational multiple of the length

Aplikace matematiky (1988)

- Volume: 33, Issue: 2, page 94-102
- ISSN: 0862-7940

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topFeireisl, Eduard. "On the existence of free vibrations for a beam equation when the period is an irrational multiple of the length." Aplikace matematiky 33.2 (1988): 94-102. <http://eudml.org/doc/15527>.

@article{Feireisl1988,

abstract = {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.},

author = {Feireisl, Eduard},

journal = {Aplikace matematiky},

keywords = {nonuniqueness; time-periodical solutions; semilinear equation; irrational periods; dual variational method; nonuniqueness; time-periodical solutions},

language = {eng},

number = {2},

pages = {94-102},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {On the existence of free vibrations for a beam equation when the period is an irrational multiple of the length},

url = {http://eudml.org/doc/15527},

volume = {33},

year = {1988},

}

TY - JOUR

AU - Feireisl, Eduard

TI - On the existence of free vibrations for a beam equation when the period is an irrational multiple of the length

JO - Aplikace matematiky

PY - 1988

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 33

IS - 2

SP - 94

EP - 102

AB - 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.

LA - eng

KW - nonuniqueness; time-periodical solutions; semilinear equation; irrational periods; dual variational method; nonuniqueness; time-periodical solutions

UR - http://eudml.org/doc/15527

ER -

## References

top- J. M. Coron, 10.1007/BF01455317, Math. Ann. 262 (1983), 273-285. (1983) Zbl0489.35061MR0690201DOI10.1007/BF01455317
- D. G. Costa M. Willem, Multiple critical points of invariant functional and applications, Séminaire de Mathématique 2-éme Semestre Université Catholique de Louvain. Zbl0628.35037
- I. Ekeland R. Temam, Convex analysis and variational problems, North-Holland Publishing Company 1976. (1976) Zbl0322.90046MR0463994
- 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. (1971) Zbl0226.35008MR0289918

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