Numerical mountain pass solutions of a suspension bridge equation

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Cited by (39)

  • Multiple periodic solutions for suspension bridge systems

    2019, Journal of Mathematical Analysis and Applications
  • Random attractors for the coupled suspension bridge equations with white noises

    2017, Applied Mathematics and Computation
    Citation Excerpt :

    In [2], Ahmed and Harbi proved the existence and uniqueness of the weak solution for the Cauchy problem of the deterministic coupled suspension bridge equations. Similar models have also been presented and considered by other some authors, but most of them were concentrated on either existence and decay estimates of solutions, or the approximations and numerical simulations, see [3,4,9–11] and references therein. We first investigated the existence of global attractors for both the single and the coupled deterministic suspension bridge equations using the methods of the energy estimates from the infinite dimensional dynamical system view, please refer the reader to [5,12,13,15,16].

  • Random attractors for the extensible suspension bridge equation with white noise

    2015, Computers and Mathematics with Applications
    Citation Excerpt :

    Just for the suspension bridge equation (1.2), most of the earlier literatures only deal with existence of the periodic solutions and numerical simulations [4–6], while only few works were concerned with the long-time behavior of the solutions.

  • Existence of strong solutions and global attractors for the suspension bridge equations

    2007, Nonlinear Analysis, Theory, Methods and Applications
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    For the problem (1.1), there are many classical results. For instance, the existence, multiplicity and properties of the travelling wave solutions, etc., were studied by most authors; we refer the reader to [1–6] and references therein. In [1], the author listed the following open problem:

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