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Fundam. Prikl. Mat., 2002, Volume 8, Issue 3, Pages 877–886 (Mi fpm680)  

This article is cited in 6 scientific papers (total in 6 papers)

Nonlinear vibrations of a nonhomogeneous string

I. A. Rudakov

Bryansk State Pedagogical University

Abstract: 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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Bibliographic databases:
UDC: 517.946
Received: 01.04.2000

Citation: I. A. Rudakov, “Nonlinear vibrations of a nonhomogeneous string”, Fundam. Prikl. Mat., 8:3 (2002), 877–886

Citation in format AMSBIB
\Bibitem{Rud02}
\by I.~A.~Rudakov
\paper Nonlinear vibrations of a~nonhomogeneous string
\jour Fundam. Prikl. Mat.
\yr 2002
\vol 8
\issue 3
\pages 877--886
\mathnet{http://mi.mathnet.ru/fpm680}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1971879}
\zmath{https://zbmath.org/?q=an:1050.35114}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. A. Rudakov, “Periodic Solutions of a Nonlinear Wave Equation with Nonconstant Coefficients”, Math. Notes, 76:3 (2004), 395–406  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Rudakov, IA, “A nontrivial periodic solution of the nonlinear wave equation with homogeneous boundary conditions”, Differential Equations, 41:10 (2005), 1467  mathnet  crossref  mathscinet  zmath  isi  elib
    3. I. A. Rudakov, “Periodic solutions of a quasilinear wave equation with homogeneous boundary conditions”, J. Math. Sci., 150:6 (2008), 2588–2597  mathnet  crossref  mathscinet  zmath  elib
    4. I. A. Rudakov, “Nonlinear equations satisfying the nonresonance condition”, J. Math. Sci. (N. Y.), 135:1 (2006), 2749–2763  mathnet  crossref  mathscinet  zmath
    5. I. A. Rudakov, “Periodic solutions of a quasilinear wave equation with variable coefficients”, Sb. Math., 198:7 (2007), 993–1009  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. I. A. Rudakov, “Periodic solutions of a nonlinear wave equation with Neumann and Dirichlet boundary conditions”, Russian Math. (Iz. VUZ), 51:2 (2007), 44–52  mathnet  crossref  mathscinet  zmath  elib
  • Фундаментальная и прикладная математика
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