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.
@article{104290,
author = {Eduard Feireisl},
title = {Free vibrations for the equation of a rectangular thin plate},
journal = {Applications of Mathematics},
volume = {33},
year = {1988},
pages = {81-93},
zbl = {0648.73024},
mrnumber = {0940708},
language = {en},
url = {http://dml.mathdoc.fr/item/104290}
}
Feireisl, Eduard. Free vibrations for the equation of a rectangular thin plate. Applications of Mathematics, Tome 33 (1988) pp. 81-93. http://gdmltest.u-ga.fr/item/104290/
Some applications of monotone operator theory to resonance problems, Nonlinear Anal. 3 (1979), 815-830. (1979) | Article | MR 0548954
Nontrivial periodic solutions of a nonlinear beam equation, Math. Meth. in the Appl. Sci. 4 (1982), 194-205. (1982) | Article | MR 0659037
On periodic solutions of a beam equation, (Czech.). Thesis, Fac. Math. Phys. of Charles Univ., Prague 1982. (1982)
Free vibrations for the equation $u_{tt} - u_{xx} + f(u) = 0$ with f sublinear, Proceedings of EQUADIFF 5, Teubner Texte zur Mathematik, Band 47, 228-230. | MR 0715981
Free vibrations for a semilinear wave equation, Comm. Pure Appl. Math. 31 (1978), 31-68. (1978) | Article | MR 0470378 | Zbl 0341.35051