Geodesic
Periodic solutions of a non-linear wave equation with homogeneous boundary conditions
Izvestiya. Mathematics , Tome 70 (2006) no. 1, pp. 109-120.

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We prove the existence of time-periodic solutions of a non-linear wave equation with homogeneous boundary conditions. The non-linear term either has polynomial growth or satisfies a “non-resonance” condition. 
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I. A. Rudakov. Periodic solutions of a non-linear wave equation with homogeneous boundary conditions. Izvestiya. Mathematics , Tome 70 (2006) no. 1, pp. 109-120. http://geodesic.mathdoc.fr/item/IM2_2006_70_1_a4/

[1] Brezis H., Nirenberg L., “Forced vibrations for a nonlinear wave equations”, Comm. Pure Appl. Math., 31:1 (1978), 1–30 | MR | Zbl

[2] Bahri A., Brezis H., “Periodic solution of a nonlinear wave equation”, Proc. Roy. Soc. Edinburgh Sect. A, 85 (1980), 313–320 | MR | Zbl

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

[4] Plotnikov P. I., “Suschestvovanie schetnogo mnozhestva periodicheskikh reshenii zadachi o vynuzhdennykh kolebaniyakh dlya slabo nelineinogo volnovogo uravneniya”, Matem. sb., 136(178):4(8) (1988), 546–560 | MR | Zbl

[5] Rudakov I. A., “Nelineinye kolebaniya struny”, Vestn. Mosk. un-ta. Ser. 1. Matem. Mekhan., 1984, no. 2, 9–13 | MR | Zbl

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

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

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

[9] Fadell E. R., Husseini S. Y., Rabinowitz P. H., “Borsuk–Ulam theorems for arbitrary $S^1$ actions and applications”, Trans. Amer. Math. Soc., 274:1 (1982), 345–360 | DOI | MR | Zbl