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Small time-periodic solutions to a nonlinear equation of a vibrating string. (English) Zbl 0653.35063
Making use of the accelerated convergence method the author proves existence of at least one $$\omega$$-periodic $$(u_ 1,u_ 2)$$ to the system $u_{1tt}+\sigma_ 1(u_{1x},u_{2x},u_{1xx},u_{1t})=f_ 1,\quad -u_{2xx}+\sigma_ 2(u_{1x},u_{1xx})=f_ 2$ with Dirichlet boundary conditions where $$f_ j$$ are $$\omega$$-periodic in t, small and sufficiently smooth. In a special case, the system above reduces to an integrodifferential equation describing vibrations of a damped extensive string.
Reviewer: O.Vejvoda

##### MSC:
 35L70 Second-order nonlinear hyperbolic equations 35B10 Periodic solutions to PDEs
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##### References:
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