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Existence of bounded solutions on the real line for Liénard system

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Abstract

The existence of monotone and non-monotone solutions of boundary value problem on the real line for Liénard equation is studied. Applying the theory of planar dynamical systems and the comparison method of vector fields defined by Liénard system and the system given by symmetric transformation or quasi-symmetric transformation, the invariant regions of the system are constructed. The existence of connecting orbits can be proved. A lot of sufficient conditions to guarantee the existence of solutions of the boundary value problem are obtained. Especially, when the source function is bi-stable, the existence of infinitely many monotone solusion is obtained.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Ningbo University, 315211, Ningbo, Zhejiang, P. R. China

    Xiao Hai-bin

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  1. Xiao Hai-bin
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Communicated by Lupi Ji-bin

Biography: Xupiao Hai-bin (1973−), Master

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Hai-bin, X. Existence of bounded solutions on the real line for Liénard system. Appl Math Mech 24, 479–490 (2003). https://doi.org/10.1007/BF02439628

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  • DOI: https://doi.org/10.1007/BF02439628

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