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Boundedness of semilinear Duffing equations with singularity

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Abstract

We prove the boundedness of all solutions for the equation x″ + V′(x) = D x G(x, t), where V (x) is of singular potential, i.e., lim x→−1 V (x) = +∞, and G(x, t) is bounded and periodic in t. We give sufficient conditions on V (x) and G(x, t) to ensure that all solutions are bounded.

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Authors and Affiliations

  1. School of Mathematics and Statistics, YiLi Normal University, Yining, 835000, China

    Xiumei Xing

  2. School of Science, Nanjing University of Science and Technology, Nanjing, 210094, China

    Lei Jiao

Authors
  1. Xiumei Xing
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  2. Lei Jiao
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Correspondence to Lei Jiao.

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Xing, X., Jiao, L. Boundedness of semilinear Duffing equations with singularity. Front. Math. China 9, 1427–1452 (2014). https://doi.org/10.1007/s11464-014-0424-0

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  • DOI: https://doi.org/10.1007/s11464-014-0424-0

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