dc.contributor.authorZhang, Ziheng
dc.contributor.authorLiao, Fang-Fang
dc.contributor.authorWong, Patricia J. Y.
dc.identifier.citationZhang, Z., Liao, F.-F., & Wong, P. J. Y. (2014). Homoclinic Solutions for a Class of Second Order Nonautonomous Singular Hamiltonian Systems. Abstract and Applied Analysis, 2014, 829052-.en_US
dc.description.abstractWe are concerned with the existence of homoclinic solutions for the following second order nonautonomous singular Hamiltonian systems ̈ 𝑢??? + 𝑎??? ( 𝑡??? ) 𝑊??? 𝑢??? ( 𝑢??? ) = 0 , (HS) where − ∞ < 𝑡??? < + ∞ , 𝑢??? = ( 𝑢??? 1 , 𝑢??? 2 , … , 𝑢??? 𝑁??? ) ∈ ℝ 𝑁??? ( 𝑁??? ≥ 3 ) , 𝑎??? ∶ ℝ → ℝ is a continuous bounded function, and the potential 𝑊??? ∶ ℝ 𝑁??? \ { 𝜉??? } → ℝ has a singularity at 0 ≠ 𝜉??? ∈ ℝ 𝑁??? , and 𝑊??? 𝑢??? ( 𝑢??? ) is the gradient of 𝑊??? at 𝑢??? . The novelty of this paper is that, for the case that 𝑁??? ≥ 3 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 𝑊??? . Different from the cases that (HS) is autonomous ( 𝑎??? ( 𝑡??? ) ≡ 1 ) 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 𝑁??? ≥ 3 . Besides the usual conditions on 𝑊??? , we need the assumption that 𝑎???  ( 𝑡??? ) < 0 for all 𝑡??? ∈ ℝ to guarantee the existence of homoclinic solution. Recent results in the literature are generalized and significantly improved.en_US
dc.relation.ispartofseriesAbstract and applied analysisen_US
dc.rights© 2014 Ziheng Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.en_US
dc.subjectDRNTU::Engineering::Electrical and electronic engineering
dc.titleHomoclinic solutions for a class of second order nonautonomous singular Hamiltonian systemsen_US
dc.typeJournal Article
dc.contributor.schoolSchool of Electrical and Electronic Engineeringen_US
dc.description.versionPublished versionen_US

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