Frontiers of Mathematics in China >

2014 , Vol. 9 >Issue 6: 1427 - 1452

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

RESEARCH ARTICLE

Boundedness of semilinear Duffing equations with singularity

  • Xiumei XING 1 ,
  • Lei JIAO , 2
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  • 1. School of Mathematics and Statistics, YiLi Normal University, Yining 835000, China
  • 2. School of Science, Nanjing University of Science and Technology, Nanjing 210094, China

Received date: 20 Dec 2011

Accepted date: 04 Aug 2014

Published date: 29 Oct 2014

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

We prove the boundedness of all solutions for the equation x″ + V′(x) = DxG(x, t), where V(x) is of singular potential, i.e., limx→-1V(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.

Key words： Hamiltonian system; repulsive singularity; boundedness of solutions; canonical transformation; Moser’s small twist theorem

Cite this article

Xiumei XING , Lei JIAO . Boundedness of semilinear Duffing equations with singularity[J]. Frontiers of Mathematics in China, 2014 , 9(6) : 1427 -1452 . DOI: 10.1007/s11464-014-0424-0

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