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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     author = {I. A. Rudakov},
     title = {Periodic solutions of a non-linear wave equation with homogeneous boundary conditions},
     journal = {Izvestiya. Mathematics },
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     number = {1},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2006_70_1_a4/}
}
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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/