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 ApplicationsAn iterative kernel based method for fourth order nonlinear equation with nonlinear boundary condition
2018, Communications in Nonlinear Science and Numerical SimulationRandom attractors for the coupled suspension bridge equations with white noises
2017, Applied Mathematics and ComputationCitation 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 ApplicationsCitation 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 coupled suspension bridge equations
2009, Journal of Differential EquationsExistence of strong solutions and global attractors for the suspension bridge equations
2007, Nonlinear Analysis, Theory, Methods and ApplicationsCitation Excerpt :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: