![](/images/graphics-bg.png)
Homoclinic Solutions for a Class of Second Order Nonautonomous Singular Hamiltonian Systems
Joint Authors
Liao, Fang-fang
Zhang, Ziheng
Wong, Patricia J. Y.
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-02-19
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
We 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.
American Psychological Association (APA)
Zhang, Ziheng& Liao, Fang-fang& Wong, Patricia J. Y.. 2014. Homoclinic Solutions for a Class of Second Order Nonautonomous Singular Hamiltonian Systems. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-1014862
Modern Language Association (MLA)
Zhang, Ziheng…[et al.]. Homoclinic Solutions for a Class of Second Order Nonautonomous Singular Hamiltonian Systems. Abstract and Applied Analysis No. 2014 (2014), pp.1-8.
https://search.emarefa.net/detail/BIM-1014862
American Medical Association (AMA)
Zhang, Ziheng& Liao, Fang-fang& Wong, Patricia J. Y.. Homoclinic Solutions for a Class of Second Order Nonautonomous Singular Hamiltonian Systems. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-1014862
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1014862