FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2002, VOLUME 8, NUMBER 3, PAGES 877-886

**Nonlinear vibrations of a nonhomogeneous string**

I. A. Rudakov

Abstract

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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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Location: http://mech.math.msu.su/~fpm/eng/k02/k023/k02314h.htm

Last modified: February 17, 2003