International Journal of Wireless and Microwave Technologies (IJWMT)
IJWMT Vol. 1, No. 5, 15 Oct. 2011
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The Existence of Homoclinic Solutions for Second Order Hamiltonian System
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Author(s)
Jie Gao
1,*
Index Terms
Homoclinic solution, Hamiltonian system, critical point, （PS） condition
Abstract
The research of homoclinic orbits for Hamiltonian system is a classical problem, it has valuable applications in celestial mechanics, plasma physis, and biological engineering. For example, homoclinic orbits rupture can yield chaos lead to more complex dynamics behaviour. This paper studies the existence of homoclinic solutions for a class of second order Hamiltonian system, we will prove this system exists at least one nontrivial homoclinic solution.
Cite This Paper
Jie Gao,"The Existence of Homoclinic Solutions for Second Order Hamiltonian System", IJWMT, vol.1, no.5, pp.54-59, 2011. DOI: 10.5815/ijwmt.2011.05.08
Reference
[1]H. Poincaré, "les méthodes nouvelles de la mécanique céleste", Gauthier-villars, pairs, pp.1897-1899 .
[2]E. Paturel, "Multiple homoclinic orbits for a class of Hamiltonian systems", Calc. Val. Partial Differential Equations, 12(2001),no.2, pp.117-143
[3]A. Flavia, "Periodic and homoclinic solutions to a class of Hamiltonian systems with indefinite potential in sign", Boll.Un. Mat. Ital., B(7)10(1996), no.2, pp.303-324.
[4]M. Izydorek and J. Junczewska, "Homoclinic solutions for a class of the second order hamiltonian systems", J. Differential Equations, 219(2005), no.2, pp.375-389.
[5]Q. Zhang and C. Liu, "Infinitely many homoclinic solutions for second order Hamiltonian systems", Nonlinear Anal., 72(2010),pp.894-903.
[6]W. Omana and M. Willem, "Homoclinic orbits for a class of Hamiltonian systems", Differential Integral Equations, 5(1992), no.5, pp.1115-1120.
[7]Z. Zhang and R. Yuan, "Homoclinic solutions for a class of non-autonomous subquadratic second-order Hamiltonian systems", Nonlinear Analysis, 71(2009), pp.4125-4130.
[8]P. H. Rabinowitz, "Minimax Methods in Critical Point Theory with Applications to Differential Equations", CBMS Reg.Conf. Ser. in. Math., vol. 65, America Mathematical society, Provodence, RI, 1986