nonlinear string equation; accelerated convergence; existence; periodic; Dirichlet boundary conditions; vibrations; damped extensive string; time-periodic solution
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.
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. Comment. Math. Univ. Carolinae 25 (1984), pp. 519-536. MR 0775567
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 O. Vejvoda, et al.: Partial differential equations: Time-periodic Solutions
. Martinus Nijhoff Publ., 1982. Zbl 0501.35001