Geodesic
Periodic Solutions of the Quasilinear Equation of Forced Vibrations of an Inhomogeneous String
Matematičeskie zametki, Tome 101 (2017) no. 1, pp. 116-129

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The existence of an infinite number of periodic solutions of a quasilinear wave equation with variable coefficients, with Dirichlet and Neumann boundary conditions on the closed interval and with time-periodic right-hand side is proved. The nonlinear summand has a power-law growth.
Keywords: wave equation, periodic solutions, variational method, perturbation of even functionals. 
@article{MZM_2017_101_1_a10,
     author = {I. A. Rudakov},
     title = {Periodic {Solutions} of the {Quasilinear} {Equation} of {Forced} {Vibrations} of an {Inhomogeneous} {String}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {116--129},
     publisher = {mathdoc},
     volume = {101},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_101_1_a10/}
}
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I. A. Rudakov. Periodic Solutions of the Quasilinear Equation of Forced Vibrations of an Inhomogeneous String. Matematičeskie zametki, Tome 101 (2017) no. 1, pp. 116-129. http://geodesic.mathdoc.fr/item/MZM_2017_101_1_a10/