W-stability theorems of nonlinear impulsive functional differential systems

This paper studies the W-stability of the solutions of nonlinear impulsive functional differential systems by using Lyapunov functions and Razumikhin technique. Some results that guarantee the W-stability and W-uniform stability are obtained here. And the asymptotical stability criteria of nonlinear impulsive functional differential systems are then established by using the W-uniform stability, which show the advantages of the obtained results.

[1]  Jianhua Shen,et al.  Razumikhin type stability theorems for impulsive functional differential equations 1 1 Research was , 1998 .

[2]  Xinzhi Liu,et al.  Existence, uniqueness and boundedness results for impulsive delay differential equations , 2000 .

[3]  Jianhua Shen Razumikhin techniques in impulsive functional differential equations , 1999 .

[4]  Xinzhi Liu,et al.  Boundedness for impulsive delay differential equations and applications to population growth models , 2003 .

[5]  A. Ouahab Local and global existence and uniqueness results for impulsive functional differential equations with multiple delay , 2006 .

[6]  Ivanka M. Stamova,et al.  Lyapunov—Razumikhin method for impulsive functional differential equations and applications to the population dynamics , 2001 .

[7]  J. Hale Theory of Functional Differential Equations , 1977 .

[8]  Yepeng Xing,et al.  A new approach to stability of impulsive functional differential equations , 2004, Appl. Math. Comput..

[9]  Stability of the solutions of impulsive functional-differential equations by Lyapunov's direct method , 2001, The ANZIAM Journal.

[10]  V. Lakshmikantham,et al.  Theory of Impulsive Differential Equations , 1989, Series in Modern Applied Mathematics.

[11]  Xinzhi Liu,et al.  Uniform boundedness and stability criteria in terms of two measures for impulsive integro-differential equations , 1999, Appl. Math. Comput..

[12]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.