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Mat. Zametki, 2004, Volume 76, Issue 3, Pages 427–438 (Mi mz119)  

This article is cited in 15 scientific papers (total in 15 papers)

Periodic Solutions of a Nonlinear Wave Equation with Nonconstant Coefficients

I. A. Rudakov

M. V. Lomonosov Moscow State University

Abstract: The existence of time-periodic solutions of a nonlinear equation for forced oscillations of a bounded string is proved when the d'Alembert operator has nonconstant coefficients and the nonlinear term has power-law growth.


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English version:
Mathematical Notes, 2004, 76:3, 395–406

Bibliographic databases:

UDC: 517.946
Received: 17.01.2003
Revised: 30.01.2004

Citation: I. A. Rudakov, “Periodic Solutions of a Nonlinear Wave Equation with Nonconstant Coefficients”, Mat. Zametki, 76:3 (2004), 427–438; Math. Notes, 76:3 (2004), 395–406

Citation in format AMSBIB
\by I.~A.~Rudakov
\paper Periodic Solutions of a Nonlinear Wave Equation with Nonconstant Coefficients
\jour Mat. Zametki
\yr 2004
\vol 76
\issue 3
\pages 427--438
\jour Math. Notes
\yr 2004
\vol 76
\issue 3
\pages 395--406

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. A. Rudakov, “Nonlinear equations satisfying the nonresonance condition”, J. Math. Sci. (N. Y.), 135:1 (2006), 2749–2763  mathnet  crossref  mathscinet  zmath
    2. 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
    3. 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
    4. Baldi P., Berti M., “Forced vibrations of a nonhomogeneous string”, SIAM J. Math. Anal., 40:1 (2008), 382–412  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    5. Ji Shuguan, “Time periodic solutions to a nonlinear wave equation with $x$-dependent coefficients”, Calc. Var. Partial Differential Equations, 32:2 (2008), 137–153  crossref  mathscinet  zmath  isi  scopus  scopus
    6. V. A. Kondrat'ev, I. A. Rudakov, “Periodic Solutions of a Quasilinear Wave Equation”, Math. Notes, 85:1 (2009), 34–50  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. Ji Shuguan, “Time-periodic solutions to a nonlinear wave equation with periodic or anti-periodic boundary conditions”, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 465:2103 (2009), 895–913  crossref  mathscinet  zmath  isi  scopus  scopus
    8. Ji Shuguan, “Periodic solutions on the Sturm–Liouville boundary value problem for two-dimensional wave equation”, J. Math. Phys., 50:11 (2009), 113510, 16 pp.  crossref  mathscinet  zmath  isi  scopus  scopus
    9. I. A. Rudakov, “On time-periodic solutions of a quasilinear wave equation”, Proc. Steklov Inst. Math., 270 (2010), 222–229  mathnet  crossref  mathscinet  zmath  isi  elib
    10. Ji Sh., Li Y., “Time Periodic Solutions to the One-Dimensional Nonlinear Wave Equation”, Arch Ration Mech Anal, 199:2 (2011), 435–451  crossref  mathscinet  zmath  isi  elib  scopus
    11. Ji Sh., Gao Ya., Zhu W., “Existence and Multiplicity of Periodic Solutions for Dirichlet?Neumann Boundary Value Problem of a Variable Coefficient Wave Equation”, Adv. Nonlinear Stud., 16:4 (2016), 765–773  crossref  mathscinet  zmath  isi  elib  scopus
    12. Rudakov I.A., “Periodic solutions of the wave equation with nonconstant coefficients and with homogeneous Dirichlet and Neumann boundary conditions”, Differ. Equ., 52:2 (2016), 248–257  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    13. I. A. Rudakov, “Periodic Solutions of the Quasilinear Equation of Forced Vibrations of an Inhomogeneous String”, Math. Notes, 101:1 (2017), 137–148  mathnet  crossref  crossref  mathscinet  isi  elib
    14. Ji Sh., “Periodic Solutions For One Dimensional Wave Equation With Bounded Nonlinearity”, J. Differ. Equ., 264:9 (2018), 5527–5540  crossref  mathscinet  zmath  isi
    15. Ma M., Ji Sh., “Time Periodic Solutions of One-Dimensional Forced Kirchhoff Equations With X-Dependent Coefficients”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 474:2213 (2018), 20170620  crossref  isi  scopus  scopus
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