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Homoclinic Solutions for a Class of Second Order Nonautonomous Singular Hamiltonian Systems

Author

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  • Ziheng Zhang
  • Fang-Fang Liao
  • Patricia J. Y. Wong

Abstract

We are concerned with the existence of homoclinic solutions for the following second order nonautonomous singular Hamiltonian systems , (HS) where , , is a continuous bounded function, and the potential has a singularity at , and is the gradient of at . The novelty of this paper is that, for the case that and (HS) is nonautonomous (neither periodic nor almost periodic), we show that (HS) possesses at least one nontrivial homoclinic solution. Our main hypotheses are the strong force condition of Gordon and the uniqueness of a global maximum of . Different from the cases that (HS) is autonomous or (HS) is periodic or almost periodic, as far as we know, this is the first result concerning the case that (HS) is nonautonomous and . Besides the usual conditions on , we need the assumption that for all to guarantee the existence of homoclinic solution. Recent results in the literature are generalized and significantly improved.

Suggested Citation

  • Ziheng Zhang & Fang-Fang Liao & Patricia J. Y. Wong, 2014. "Homoclinic Solutions for a Class of Second Order Nonautonomous Singular Hamiltonian Systems," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, February.
    • Handle: RePEc:hin:jnlaaa:829052
    DOI: 10.1155/2014/829052
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