Article
MSC:
35B10,
35L70,
58E05,
73K12,
74H45,
74K20 | MR 0940708 | Zbl 0648.73024 | DOI: 10.21136/AM.1988.104290
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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
Summary:
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.
References:
[1] H. Amann G. Mancini: Some applications of monotone operator theory to resonance problems. Nonlinear Anal. 3 (1979), 815-830. DOI 10.1016/0362-546X(79)90050-6 | MR 0548954
[2] K. C. Chang L. Sanchez: Nontrivial periodic solutions of a nonlinear beam equation. Math. Meth. in the Appl. Sci. 4 (1982), 194-205. DOI 10.1002/mma.1670040113 | MR 0659037
[3] E. Feireisl: On periodic solutions of a beam equation. (Czech.). Thesis, Fac. Math. Phys. of Charles Univ., Prague 1982.
[4] V. Lovicar: 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
[5] P. H. Rabinowitz: Free vibrations for a semilinear wave equation. Comm. Pure Appl. Math. 31 (1978), 31-68. DOI 10.1002/cpa.3160310103 | MR 0470378 | Zbl 0341.35051
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