Geodesic
Periodic Solutions of a Nonlinear Wave Equation with Nonconstant Coefficients
Matematičeskie zametki, Tome 76 (2004) no. 3, pp. 427-438

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The existence of time-periodic solutions of a nonlinear equation for forced oscillations of a bounded string is proved when the d'Alembert operator has nonconstant coefficients and the nonlinear term has power-law growth. 
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     author = {I. A. Rudakov},
     title = {Periodic {Solutions} of a {Nonlinear} {Wave} {Equation} with {Nonconstant} {Coefficients}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {427--438},
     publisher = {mathdoc},
     volume = {76},
     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_76_3_a11/}
}
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I. A. Rudakov. Periodic Solutions of a Nonlinear Wave Equation with Nonconstant Coefficients. Matematičeskie zametki, Tome 76 (2004) no. 3, pp. 427-438. http://geodesic.mathdoc.fr/item/MZM_2004_76_3_a11/