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Mathematics > Dynamical Systems

arXiv:1804.03300 (math)
[Submitted on 10 Apr 2018]

Title:Periodic Solutions to Nonlinear Euler-Bernoulli Beam Equations

Authors:Bochao Chen, Yixian Gao, Yong Li
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Abstract:Bending vibrations of thin beams and plates may be described by nonlinear Euler-Bernoulli beam equations with $x$-dependent coefficients. In this paper we investigate existence of families of time-periodic solutions to such a model using Lyapunov-Schmidt reduction and a differentiable Nash-Moser iteration scheme. The results hold for all parameters $(\epsilon,\omega)$ in a Cantor set with asymptotically full measure as $\epsilon\rightarrow0$.
Comments: 29 pages
Subjects: Dynamical Systems (math.DS)
MSC classes: 35B10, 58C15, 58J45, 35L72
Cite as: arXiv:1804.03300 [math.DS]
  (or arXiv:1804.03300v1 [math.DS] for this version)
  https://doi.org/10.48550/arXiv.1804.03300

Submission history

From: Yixian Gao [view email]
[v1] Tue, 10 Apr 2018 01:23:49 UTC (40 KB)
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