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.
@article{104278,
author = {Eduard Feireisl},
title = {Small time-periodic solutions to a nonlinear equation of a vibrating string},
journal = {Applications of Mathematics},
volume = {32},
year = {1987},
pages = {480-490},
zbl = {0653.35063},
mrnumber = {0916063},
language = {en},
url = {http://dml.mathdoc.fr/item/104278}
}
Feireisl, Eduard. Small time-periodic solutions to a nonlinear equation of a vibrating string. Applications of Mathematics, Tome 32 (1987) pp. 480-490. http://gdmltest.u-ga.fr/item/104278/
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