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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{IM2_2015_79_5_a8,
     author = {I. A. Rudakov},
     title = {Periodic solutions of the quasilinear equation of forced beam vibrations with homogeneous boundary conditions},
     journal = {Izvestiya. Mathematics },
     pages = {1064--1086},
     publisher = {mathdoc},
     volume = {79},
     number = {5},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2015_79_5_a8/}
}
TY  - JOUR
AU  - I. A. Rudakov
TI  - Periodic solutions of the quasilinear equation of forced beam vibrations with homogeneous boundary conditions
JO  - Izvestiya. Mathematics 
PY  - 2015
SP  - 1064
EP  - 1086
VL  - 79
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2015_79_5_a8/
LA  - en
ID  - IM2_2015_79_5_a8
ER  - 
%0 Journal Article
%A I. A. Rudakov
%T Periodic solutions of the quasilinear equation of forced beam vibrations with homogeneous boundary conditions
%J Izvestiya. Mathematics 
%D 2015
%P 1064-1086
%V 79
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2015_79_5_a8/
%G en
%F IM2_2015_79_5_a8
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/

[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