Periodic solutions of a class of impulsive neutral delay differential equation

Abstract A class of impulsive neutral delay differential equation is studied. By using fixed point theorem in cone, some sufficient conditions of the existence for multiple periodic solutions are obtained. Some known results are generalized. Two examples are also given to support our main results.

[1]  N. Youssef POSITIVE PERIODIC SOLUTIONS OF SYSTEMS OF FUNCTIONAL DIFFERENTIAL EQUATIONS , 2005 .

[2]  Y. Raffoul,et al.  Positive periodic solutions of functional discrete systems and population models , 2005 .

[3]  Ju H. Park,et al.  Augmented Lyapunov functional approach to stability of uncertain neutral systems with time-varying delays , 2009, Appl. Math. Comput..

[4]  Ju H. Park,et al.  Novel robust stability criterion for a class of neutral systems with mixed delays and nonlinear perturbations , 2005, Appl. Math. Comput..

[5]  Yong-Kui Chang,et al.  Controllability of impulsive neutral functional differential inclusions with infinite delay in Banach spaces , 2009 .

[6]  Leo F. Boron,et al.  Positive solutions of operator equations , 1964 .

[7]  Ju H. Park,et al.  On stability criteria for uncertain delay-differential systems of neutral type with time-varying delays , 2008, Appl. Math. Comput..

[8]  Hai-Feng Huo,et al.  Existence and global attractivity of positive periodic solution of an impulsive delay differential equation , 2004 .

[9]  J. Hale Functional Differential Equations , 1971 .

[10]  Yong-Kui Chang,et al.  Controllability of impulsive functional differential systems with infinite delay in Banach spaces , 2007 .

[11]  Ju H. Park,et al.  Robust guaranteed cost control for uncertain linear differential systems of neutral type , 2003, Appl. Math. Comput..

[12]  Jurang Yan,et al.  Existence of positive periodic solutions for an impulsive differential equation , 2008 .

[13]  Guangzhao Zeng,et al.  Existence of periodic solution of order one of planar impulsive autonomous system , 2006 .

[14]  Guirong Liu,et al.  Existence and global attractivity of unique positive periodic solution for a Lasota–Wazewska model , 2006 .

[15]  Wan-Tong Li,et al.  Existence of positive periodic solution of a neutral impulsive delay predator-prey system , 2007, Appl. Math. Comput..

[16]  Hai-Feng Huo Existence of positive periodic solutions of a neutral delay Lotka-Volterra system with impulses , 2004 .