Geodesic
Periodic solutions of the quasilinear equation of forced beam vibrations with homogeneous boundary conditions
Izvestiya. Mathematics, Tome 79 (2015) no. 5, pp. 1064-1086

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We prove the existence of a countable family of time-periodic solutions of the quasilinear equation of beam vibrations with homogeneous boundary conditions and time-periodic right-hand side in the case when the non-linear term has power growth.
Keywords: beam vibrations, time-periodic solution, variational method, perturbation of even functionals. 
I. A. Rudakov. Periodic solutions of the quasilinear equation of forced beam vibrations with homogeneous boundary conditions. Izvestiya. Mathematics, Tome 79 (2015) no. 5, pp. 1064-1086. http://geodesic.mathdoc.fr/item/IM2_2015_79_5_a8/
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[1] V. M. Babich, N. S. Grigoreva, Ortogonalnye razlozheniya i metod Fure, Izd-vo Leningr. un-ta, L., 1983, 240 pp. | MR | Zbl

[2] V. P. Pikulin, S. I. Pohozaev, Equations in mathematical physics. A practical course, Birkhäuser Verlag, Basel, 2001, viii+207 pp. | MR | Zbl

[3] L. Collatz, Eigenwertaufgaben mit technischen Anwendungen, Zweite, durchgesehene Aufl., Akademische Verlagsgesellschaft Geest Portig K.-G., Leipzig, 1963, xiv+500 pp. | MR | MR | Zbl | Zbl

[4] E. Feireisl, “Time periodic solutions to a semilinear beam equation”, Nonlinear Anal., 12:3 (1988), 279–290 | DOI | MR | Zbl

[5] K. C. Chang, L. Sanchez, “Nontrivial periodic solutions of a nonlinear beam equation”, Math. Methods Appl. Sci., 4:1 (1982), 194–205 | DOI | MR | Zbl

[6] I. A. Rudakov, “Nonlinear equations satisfying the nonresonance condition”, J. Math. Sci. (N. Y.), 135:1 (2006), 2749–2763 | DOI | MR | Zbl

[7] I. A. Rudakov, “Periodic solutions of the quasilinear beam vibration equation with homogeneous boundary conditions”, Differ. Equ., 48:6 (2012), 820–831 | DOI | MR | Zbl

[8] P. H. Rabinowitz, “Multiple critical points of perturbed symmetric functionals”, Trans. Amer. Math. Soc., 272:2 (1982), 753–769 | DOI | MR | Zbl

[9] K. Tanaka, “Infinitely many periodic solutions for the equation: $u_{tt}-u_{xx}\pm|u|^{p-1}u=f(x,t)$. II”, Trans. Amer. Math. Soc., 307:2 (1988), 615–645 | DOI | MR | Zbl

[10] A. Bahri, H. Berestycki, “A perturbation method in critical point theory and applications”, Trans. Amer. Math. Soc., 267:1 (1981), 1–32 | DOI | MR | Zbl

[11] J. T. Schwartz, Nonlinear functional analysis, Notes on Mathematics and its Applications, Gordon and Breach Science Publishers, New York–London–Paris, 1969, vii+236 pp. | MR | Zbl

[12] V. A. Sadovnichii, Teoriya operatorov, 4-e izd., Drofa, M., 2001, 384 pp. | MR | Zbl

[13] J. Bergh, J. Löfström, Interpolation spaces. An introduction, Grundlehren Math. Wiss., 223, Springer-Verlag, Berlin–New York, 1976, x+207 pp. | MR | MR | Zbl