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Izv. RAN. Ser. Mat., 2015, Volume 79, Issue 5, Pages 215–238 (Mi izv8250)  

This article is cited in 3 scientific papers (total in 3 papers)

Periodic solutions of the quasilinear equation of forced beam vibrations with homogeneous boundary conditions

I. A. Rudakovab

a N. E. Bauman Moscow State Technical University
b Moscow State Aviation Technological University, Moscow

Abstract: We prove the existence of a countable family of time-periodic solutions of the quasilinear equation of beam vibrations with homogeneous boundary conditions and time-periodic right-hand side in the case when the non-linear term has power growth.

Keywords: beam vibrations, time-periodic solution, variational method, perturbation of even functionals.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.264.2014
This paper was written with the financial support of the Ministry of Education and Science of the Russian Federation (grant no. 1.264.2014).


DOI: https://doi.org/10.4213/im8250

Full text: PDF file (629 kB)
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English version:
Izvestiya: Mathematics, 2015, 79:5, 1064–1086

Bibliographic databases:

UDC: 517.954
MSC: 35B10, 35L35, 35L77
Received: 30.04.2014
Revised: 27.11.2014

Citation: I. A. Rudakov, “Periodic solutions of the quasilinear equation of forced beam vibrations with homogeneous boundary conditions”, Izv. RAN. Ser. Mat., 79:5 (2015), 215–238; Izv. Math., 79:5 (2015), 1064–1086

Citation in format AMSBIB
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Linking options:
  • http://mi.mathnet.ru/eng/izv8250
  • https://doi.org/10.4213/im8250
  • http://mi.mathnet.ru/eng/izv/v79/i5/p215

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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 the Quasilinear Equation of Forced Vibrations of an Inhomogeneous String”, Math. Notes, 101:1 (2017), 137–148  mathnet  crossref  crossref  mathscinet  isi  elib
    2. I. A. Rudakov, “On periodic solutions of a beam vibration equation”, Differ. Equ., 54:5 (2018), 687–695  crossref  crossref  isi  elib  elib  scopus
    3. I. A. Rudakov, “Equation for beam oscillations with fixed and simply supported ends”, Moscow University Mathematics Bulletin, 75:2 (2020), 53–57  mathnet  crossref  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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