Geodesic
Small time-periodic solutions to a nonlinear equation of a vibrating string
Applications of Mathematics, Tome 32 (1987) no. 6, pp. 480-490.

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In this paper, the system consisting of two nonlinear equations is studied. The former is hyperbolic with a dissipative term and the latter is elliptic. In a special case, the system reduces to the approximate model for the damped transversal vibrations of a string proposed by G. F. Carrier and R. Narasimha. Taking advantage of accelerated convergence methods, the existence of at least one time-periodic solution is stated on condition that the right-hand side of the system is sufficiently small.
DOI : 10.21136/AM.1987.104278
Classification : 35B10, 35L70, 58C15, 73K03
Keywords: nonlinear string equation; accelerated convergence; existence; periodic; Dirichlet boundary conditions; vibrations; damped extensive string; time-periodic solution 
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     title = {Small time-periodic solutions to a nonlinear equation of a vibrating string},
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Feireisl, Eduard. Small time-periodic solutions to a nonlinear equation of a vibrating string. Applications of Mathematics, Tome 32 (1987) no. 6, pp. 480-490. doi : 10.21136/AM.1987.104278. http://geodesic.mathdoc.fr/articles/10.21136/AM.1987.104278/

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