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

Eduard Feireisl

Aplikace matematiky (1988)

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

Abstract

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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 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.

How to cite

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Feireisl, 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

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  1. J. M. Coron, 10.1007/BF01455317, Math. Ann. 262 (1983), 273-285. (1983) Zbl0489.35061MR0690201DOI10.1007/BF01455317
  2. 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
  3. I. Ekeland R. Temam, Convex analysis and variational problems, North-Holland Publishing Company 1976. (1976) Zbl0322.90046MR0463994
  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. (1971) Zbl0226.35008MR0289918

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