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Řeháček, Jan
On periodic solutions of a special type of the beam equation. (English). Aplikace matematiky, vol. 33 (1988), issue 1, pp. 33-40
MSC: 35B10, 35B45, 35G20, 73K12, 74H45 | MR 0934372 | Zbl 0665.35015 | DOI: 10.21136/AM.1988.104284
Keywords:
existence; time-periodic solutions; a priori estimate; Fourier method; Brouwer’s theorem; truncated system; beam equation
Summary:
The paper deals with the existence of time-periodic solutions to the beam equation, in which terms expressing torsion and damping are also considered. The existence of periodic solutions is proved in the cas of time-periodic outer forces by means of an apriori estimate and the Fourier method.
References:
[1] N. G. de Andrade: On a nonlinear Systems of Partial Differential Equations. Journal of Math. Anal. and Appl. 91 (1983), 119-130. DOI 10.1016/0022-247X(83)90097-5 | MR 0688537
[2] J. M. Ball: Initial Boundary Value Problems for an Extensible Beam. Journal of Math. Anal. and Appl. 42(1973), 61-90. MR 0319440 | Zbl 0254.73042
[3] J. Kurzweil: Ordinary Differential Equations. Elsevier, Amsterdam, 1986. MR 0929466 | Zbl 0667.34002
[4] S. P. Timošenko D. H. Young W. Weaver: Vibrations Problems in Engineering. New York 1974.
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