Free vibrations for the equation of a rectangular thin plate

Eduard Feireisl

Aplikace matematiky (1988)

  • Volume: 33, Issue: 2, page 81-93
  • ISSN: 0862-7940

Abstract

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In the paper, we deal with the equation of a rectangular thin plate with a simply supported boundary. The restoring force being an odd superlinear function of the vertical displacement, the existence of infinitely many nonzero time-periodic solutions is proved.

How to cite

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Feireisl, Eduard. "Free vibrations for the equation of a rectangular thin plate." Aplikace matematiky 33.2 (1988): 81-93. <http://eudml.org/doc/15526>.

@article{Feireisl1988,
abstract = {In the paper, we deal with the equation of a rectangular thin plate with a simply supported boundary. The restoring force being an odd superlinear function of the vertical displacement, the existence of infinitely many nonzero time-periodic solutions is proved.},
author = {Feireisl, Eduard},
journal = {Aplikace matematiky},
keywords = {thin plate; simply supported; existence; infinitely many nonzero time-periodic solutions; Ljusternik-Schnirelman theory; approximate solution; thin plate; simply supported; existence; infinitely many nonzero time- periodic solutions; Ljusternik-Schnirelman theory; approximate solution},
language = {eng},
number = {2},
pages = {81-93},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Free vibrations for the equation of a rectangular thin plate},
url = {http://eudml.org/doc/15526},
volume = {33},
year = {1988},
}

TY - JOUR
AU - Feireisl, Eduard
TI - Free vibrations for the equation of a rectangular thin plate
JO - Aplikace matematiky
PY - 1988
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 33
IS - 2
SP - 81
EP - 93
AB - In the paper, we deal with the equation of a rectangular thin plate with a simply supported boundary. The restoring force being an odd superlinear function of the vertical displacement, the existence of infinitely many nonzero time-periodic solutions is proved.
LA - eng
KW - thin plate; simply supported; existence; infinitely many nonzero time-periodic solutions; Ljusternik-Schnirelman theory; approximate solution; thin plate; simply supported; existence; infinitely many nonzero time- periodic solutions; Ljusternik-Schnirelman theory; approximate solution
UR - http://eudml.org/doc/15526
ER -

References

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  1. H. Amann G. Mancini, 10.1016/0362-546X(79)90050-6, Nonlinear Anal. 3 (1979), 815-830. (1979) MR0548954DOI10.1016/0362-546X(79)90050-6
  2. K. C. Chang L. Sanchez, 10.1002/mma.1670040113, Math. Meth. in the Appl. Sci. 4 (1982), 194-205. (1982) MR0659037DOI10.1002/mma.1670040113
  3. E. Feireisl, On periodic solutions of a beam equation, (Czech.). Thesis, Fac. Math. Phys. of Charles Univ., Prague 1982. (1982) 
  4. V. Lovicar, Free vibrations for the equation u t t - u x x + f ( u ) = 0 with f sublinear, Proceedings of EQUADIFF 5, Teubner Texte zur Mathematik, Band 47, 228-230. MR0715981
  5. P. H. Rabinowitz, 10.1002/cpa.3160310103, Comm. Pure Appl. Math. 31 (1978), 31-68. (1978) Zbl0341.35051MR0470378DOI10.1002/cpa.3160310103

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