Existence of almost periodic solutions for neutral delay difference systems

Springer Science and Business Media LLC - Tập 4 - Trang 437-462 - 2009
Qiuxiang Feng1, Rong Yuan2
1College of Statistics, Shanxi University of Finance and Economics, Taiyuan, China
2School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing, China

Tóm tắt

In this paper, the existence of almost periodic solutions is studied via the Lyapunov function. Razumikhin type theorems are established on the existence, uniqueness and uniformly asymptotic stability of almost periodic solutions. Two examples are given to explain our results.

Tài liệu tham khảo

Agarwal R P. Difference Equations and Inequalities. 2nd Ed. New York: Dekker, 2000 Cooke K L. Stability analysis for a vector disease model. Rocky Mountain J Math, 1977, 9: 31–42 Corduneanu C. Almost Periodic Functions. New York: Chelsea, 1989 Fink A M, Seifert G. Liapunov functions and almost periodic solutions for almost periodic systems. J Diff Eqns, 2969, 5: 307–313 Gopalsamy K, Mohamad S. Canonical solutions and almost periodicity in a discrete logistic equation. Appl Math Comput, 2000, 113(2–3): 305–323 Hale J K. Periodic and almost periodic solution of functional differential equations. Arch Rational Mech Anal, 1964, 15: 289–309 Hale J K. Theory of Functional Differential Equations. Berlin: Springer, 1977 Hamaya Y. Existence of an almost periodic solution in a difference equation by Liapunov functions. Nonlinear Studies, 2001, 8(3): 373–379 Hino Y. Almost periodic solutions of functional differential equations with infinite retardation. II. Tohoku Math J, 1980, 32: 525–530 Lakshmikantham V, Trigiante D. Theory of Difference Equations. New York: Academic Press, INC, 1988 Meisters G H. On almost periodic solutions of a class of differential equations. Proc Amer Math Soc, 1959, 10: 113–119 Nakajima F. Existence of almost periodic solutions by Liapunov functions. Tohoku Math J, 1975, 27: 69–74 Sawano K. Exponential asymptotic stability for functional-differential equations with infinite retardations. Tohoku Math J, 1979, 31: 363–382 Yang X, Yuan R. On the module and spectral of almost periodic sequence in Banach space. J Beijing Normal University, 2005, 41(5): 455–459 Yoshizawa T. Extreme stability and almost periodic solutions of functional-differential equations. Arch Rational Mech Anal, 1964, 17: 148–170 Yoshizawa T. Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions. Applied Mathematical Sciences, Vol 14. Berlin: Springer-Verlag, 1975 Yuan R. Existence of almost periodic solution of functional differential equations. Ann of Diff Eqs, 1991, 7(2): 234–242 Yuan R. Existence of almost periodic solutions of functional differential equations of neutral type. J Math Anal Appl, 1992, 165(2): 524–538 Yuan R. Existence of almost periodic solutions of neutral functional-differential equations via Liapunov-Razumikhin function. Z Angew Math Phys, 1998, 49: 113–136 Yuan R. The existence of almost periodic solutions of retarded differential equations with piecewise constant argument. Nonlinear Anal, 2002, 48: 1013–1032 Yuan R, Hong J L. The existence of almost periodic solutions for a class of differential equations with piecewise constant argument. Nonlinear Analysis TMA, 1997, 28(8): 1439–1450 Zhang S. Existence of almost periodic solutions for differences systems. Ann of Diff Eqs, 2000, 16(2): 184–206 Zhang S, Liu P, Gopalsamy K. Almost periodic solutions of nonautonomous linear difference equations. Appl Anal, 2002, 81(2): 281–301 Zheng G, Zhang S. Existence of almost periodic solutions of neutral delay difference systems. Dynamics of Continuous, Discrete and Impulsive Systems, Ser A: Math Anal, 2002, 9: 523–540