Geodesic
On time-periodic solutions of a~quasilinear wave equation
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 270 (2010), pp. 226-232.

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

Existence and regularization theorems are obtained for generalized solutions of a quasilinear wave equation with variable coefficients and homogeneous Dirichlet boundary conditions. The nonlinear term either exhibits a power growth or satisfies a nonresonance condition. 
@article{TM_2010_270_a16,
     author = {I. A. Rudakov},
     title = {On time-periodic solutions of a~quasilinear wave equation},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {226--232},
     publisher = {mathdoc},
     volume = {270},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2010_270_a16/}
}
TY  - JOUR
AU  - I. A. Rudakov
TI  - On time-periodic solutions of a~quasilinear wave equation
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2010
SP  - 226
EP  - 232
VL  - 270
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2010_270_a16/
LA  - ru
ID  - TM_2010_270_a16
ER  - 
%0 Journal Article
%A I. A. Rudakov
%T On time-periodic solutions of a~quasilinear wave equation
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2010
%P 226-232
%V 270
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2010_270_a16/
%G ru
%F TM_2010_270_a16
I. A. Rudakov. On time-periodic solutions of a~quasilinear wave equation. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 270 (2010), pp. 226-232. http://geodesic.mathdoc.fr/item/TM_2010_270_a16/

[1] Brézis H., Nirenberg L., “Forced vibrations for a nonlinear wave equation”, Commun. Pure and Appl. Math., 31:1 (1978), 1–30 | DOI | MR | Zbl

[2] Rabinowitz P.H., “Free vibrations for a semilinear wave equation”, Commun. Pure and Appl. Math., 31:1 (1978), 31–68 | DOI | MR | Zbl

[3] Plotnikov P.I., “Suschestvovanie schetnogo mnozhestva periodicheskikh reshenii zadachi o vynuzhdennykh kolebaniyakh dlya slabo nelineinogo volnovogo uravneniya”, Mat. sb., 136:4 (1988), 546–560 | MR

[4] Feireisl E., “On the existence of periodic solutions of a semilinear wave equation with a superlinear forcing term”, Czech. Math. J., 38:1 (1988), 78–87 | MR | Zbl

[5] Rudakov I.A., “Nelineinye kolebaniya struny”, Vestn. Mosk. un-ta. Matematika. Mekhanika, 1984, no. 2, 9–13 | MR | Zbl

[6] Barbu V., Pavel N.H., “Periodic solutions to nonlinear one dimensional wave equation with $x$-dependent coefficients”, Trans. Amer. Math. Soc., 349:5 (1997), 2035–2048 | DOI | MR | Zbl

[7] Rudakov I.A., “Periodicheskie resheniya nelineinogo volnovogo uravneniya s nepostoyannymi koeffitsientami”, Mat. zametki., 76:3 (2004), 427–438 | DOI | MR | Zbl

[8] Rudakov I.A., “Periodicheskie resheniya kvazilineinogo volnovogo uravneniya s peremennymi koeffitsientami”, Mat. sb., 198:7 (2007), 91–108 | DOI | MR | Zbl

[9] Trikomi F., Differentsialnye uravneniya, URSS, M., 2003

[10] Babich V.M., Grigoreva N.S., Ortogonalnye razlozheniya i metod Fure, Izd-vo LGU, L., 1983 | MR | Zbl

[11] Rudakov I.A., “Periodicheskoe po vremeni reshenie uravneniya vynuzhdennykh kolebanii struny s odnorodnymi granichnymi usloviyami”, Dif. uravneniya, 39:11 (2003), 1550–1555 | MR | Zbl

[12] Rudakov I.A., “Periodicheskie resheniya nelineinogo volnovogo uravneniya s odnorodnymi granichnymi usloviyami”, Izv. RAN. Ser. mat., 70:1 (2006), 117–128 | DOI | MR | Zbl

[13] Rabinowitz P.H., “Periodic solutions of nonlinear hyperbolic partial differential equations”, Commun. Pure and Appl. Math., 20 (1967), 145–205 | DOI | MR | Zbl