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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Last modified: February 17, 2003