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

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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/}
}
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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/