Acta mathematica scientia, Series B >
HOMOCLINIC ORBITS FOR A CLASS OF THE SECOND ORDER HAMILTONIAN SYSTEMS
Received date: 2006-10-21
Revised date: 2008-03-30
Online published: 2010-01-20
Supported by
Supported by National Natural Science Foundation of China (10771173).
The existence of homoclinic orbits is obtained by the variational approach for a class of second order Hamiltonian systems q(t)+ V(t, q(t))=0, where V(t, x)=-K(t,x)+W(t, x), K(t, x) is neither a quadratic form in x nor periodic in t and W(t, x) is superquadratic in x.
WAN Li-Li , TANG Chun-Lei . HOMOCLINIC ORBITS FOR A CLASS OF THE SECOND ORDER HAMILTONIAN SYSTEMS[J]. Acta mathematica scientia, Series B, 2010 , 30(1) : 312 -318 . DOI: 10.1016/S0252-9602(10)60047-1
[1] Alves C O, Carriao P C, Miyagaki O H. Existence of homoclinic orbits for asymptotically periodic systems involving Duffing-like equation. Appl Math Lett, 2003, 16(5): 639--642
[2] Alberto Abbondandolo, Juan Molina. Index estimates for strongly indefinite functionals, periodic orbits and
homoclinic solutions of first order Hamiltonian systems. Calc Var Partial Differential Equations, 2000, 11(4): 395--430
[3] Carriao P C, Miyagaki O H. Existence of homoclinic solutions for a class of time-dependent Hamiltonian
systems. J Math Anal Appl, 1999, 230(1): 157--172
[4] Coti Zelati V, Rabinowitz P H. Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials. J Amer Math Soc, 1991, 4(4): 693--727
[5] Chen C N, Tzeng S Y. Existence and multiplicity results for homoclinic orbits of Hamiltonian systems.
Electron J Differ Equ, 1997, (7): 1--19
[6] Ding Y H. Existence and multiplicity results for homoclinic solutions to a class of Hamiltonian systems. Nonlinear Anal, 1995, 25(11): 1095--1113
[7] Hu J X. The existence of homoclinic orbits in Hamiltonian inclusions. Nonlinear Anal, Ser A: Theory Methods, 2001, 46(2): 169--180
[8] Izydorek Marek, Janczewska Joanna. Homoclinic solutions for a class of the second order Hamiltonian
systems. J Differ Equ, 2005, 219(2): 375--389
[9] Korman P, Lazer A C. Homoclinic orbits for a class of symmetric Hamiltonian systems. Electron J Differ Equ, 1994, (1): 1--10
[10] Korman P, Lazer A C, Li Yi. On homoclinic and heteroclinic orbits for Hamiltonian systems. Differential Integral Equations, 1997, 10(2): 357--368
[11] Lu Y F, Li C Y, Zhong S Z, Zhang W J. Homoclinic orbits for a class of Hamiltonian systems with potentials changing sign. Ann Differ Equ, 2005, 21(3): 370--372
[12] Omana W, Willem M. Homoclinic orbits for a class of Hamiltonian systems. Differ Integral Equ, 1992, 5(5): 1115--1120
[13] Ou Z Q, Tang C L. Existence of homoclinic solution for the second order Hamiltonian systems. J Math Anal Appl, 2004, 291(1): 203--213
[14] Rabinowitz P H. Minimax Methods in Critical Point Theory with Applications to Differential Equations. CBMS Regional Conference Series in Mathematics, Vol 65. Providence, RI: Amer Math Soc, 1986
[15] Rabinowitz P H. Homoclinic orbits for a class of Hamiltonian systems. Proc Roy Soc Edinburgh Sect A, 1990, 114(1/2): 33--38
[16] Rabinowitz P H, Tanaka K. Some results on connecting orbits for a class of Hamiltonian systems. Math Z, 1991, 206(3): 473--499
[17] Xu Xiangjin. Homoclinic orbits for first order Hamiltonian systems possessing super-quadratic potentials. Nonlinear Anal Ser A Theory Methods, 2002, 51(2): 197--214
[18] Zhao X H, Li J B, Huang K L. Homoclinic orbits in perturbed generalized Hamiltonian systems. Acta Math Sci, 1996, 16B(4): 361--374
/
| 〈 |
|
〉 |