Geodesic
Nonlinear vibrations of a~nonhomogeneous string
Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 3, pp. 877-886.

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We consider a semilinear equation for the forced vibrations of a finite string with $x$-dependent coefficients under Dirichlet boundary conditions. The existence of the time-periodic solution in nonresonant case is proved. It isn't require the Lipschitz condition. The proof uses the method of monotonic operators and principe Leray–Schauder of the fixed point. 
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I. A. Rudakov. Nonlinear vibrations of a~nonhomogeneous string. Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 3, pp. 877-886. http://geodesic.mathdoc.fr/item/FPM_2002_8_3_a13/

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