Acta mathematica scientia, Series B >
HOMOCLINIC SOLUTIONS FOR A CLASS OF SECOND ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL SYSTEMS
Received date: 2011-10-28
Revised date: 2012-12-20
Online published: 2013-09-20
Supported by
This work was sponsored by the National Natural Science Foundation of China (11271197), the Science and Technology Foundation in Ministry of Education of China (207047) and the Science Foundation of NUIST of China (20090202 and 2012r101).
By means of an extension of Mawhin´s continuation theorem and some analysis methods, the existence of a set with 2kT-periodic solutions for a class of second order neutral functional differential systems is studied, and then the homoclinic solutions are obtained as the limit points of a certain subsequence of the above set.
LU Shi-Ping , ZHENG Liang , CHEN Li-Juan . HOMOCLINIC SOLUTIONS FOR A CLASS OF SECOND ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL SYSTEMS[J]. Acta mathematica scientia, Series B, 2013 , 33(5) : 1361 -1374 . DOI: 10.1016/S0252-9602(13)60087-9
[1] Lu Shiping, Ge Weigao, Zheng Zuxiou. Periodic solutions for a kind of Rayleigh equation with a deviating argument. Appl Math Lett, 2004, 7: 443–449
[2] Lu Shiping, Ge Weigao. Some new results on the existence of Periodic solutions to a kind of Rayleigh equation with a deviating argument. Nonlinear Analysis, 2004, 56: 501–514
[3] Bouzahir Hassane, Fu Xianlong. Controllability of neutral functional differential equations with infinite delay. Acta Mathematica Scientia, 2011, 31B(1): 73–80
[4] Lu Shiping, Ge Weigao. Sufficient conditions for the existence of periodic solutions to some second order differential equations with a deviating argument. J Math Anal Appl, 2005, 308: 393–419
[5] Lu Shiping. On the existence of positive periodic solutions for neutral functional differential equation with multiple deviating arguments. J Math Anal Appl, 2003, 280: 321–333
[6] Tang X H, Lin Xiaoyan. Homoclinic solutions for a class of second-order Hamilitonian systems. J Math Anal Appl, 2009, 354: 539–549
[7] Zhang Ziheng, Yuan Rong. Homoclinic solutions for a class of non-autonomous subquadratic second-order
Hamilitonian systems. Nonlinear Analysis, 2009, 71: 4125–4130
[8] Tan X H, Xiao Li. Homoclinic solutions for nonautonomous second-order Hamiltonian systems with a coercive potential. J Math Anal Appl, 2009, 351: 586–594
[9] Izydorek M, Janczewska J. Homoclinic solutions for nonautonomous second-order Hamiltonian systems with a coercive potential. J Math Anal Appl, 2007, 335: 1119–1127
[10] Lv Xiang, Lu Shiping, Yan Ping. Homoclinic solutions for nonautonomous second-order Hamiltonian systems with a coercive potential. Nonlinear Analysis, 2010, 72: 3484–3490
[11] Lv Xiang, Lu Shiping, Yan Ping. Existence of homoclinic solutions for a class of second-order Hamiltonian systems. Nonlinear Analysis, 2010, 72: 390–398
[12] Lu Shiping. Homoclinic solutions for a nonlinear second order differential system with p-Laplacian opera-tor. Nonlinear Analysis: Real World Applications, 2011, 12: 525–534
[13] Lin Xiaobiao. Exponential dichotomies and homoclinic orbits in functional differential equations. J Differ Equ, 1986, 63: 227–254
[14] Xu Yingxiang, Huang Mingyou. Homoclinic orbits and Hopf bifurcations in delay differential systems with T.B singularity. J Differ Equ, 2008, 244: 582–598
[15] Guo Chengjun, O’Regan Donal, Xu Yuantong, Agarwal R P. Homoclinic orbits for a singular second-order neutral differential equation. J Math Anal Appl, 2010, 366: 550–560
[16] Lu Shiping. Homoclinic solutions for a class of second order p-laplacian differential systems with delay. Nonlinear Analysis: Real World Applications, 2011, 12: 780–788
[17] Rabinowitz P H. Homoclinic orbits for a class of Hamilitonian systems. Prop Roy Soc Edinburgh Sect A, 1990, 114: 33–38
[18] Lzydorek Marek, Janczewska Joanna. Homoclinic solutions for a class of the second order Hamilitonian systems. J Differ Equ, 2005, 219: 375–389
[19] Tang X H, Xiao Li. Homoclinic solutions for ordinary p-Laplacian systems with a coercive potential. Nonlinear Analysis, 2009, 71: 1124–1322
[20] Lu Shiping. Periodic solutions to a second order p-Laplacian neutral functional differential system. Non-linear Analysis, 2008, 69: 4215–4229
/
| 〈 |
|
〉 |