Invariant and attracting sets of impulsive delay difference equations with continuous variables

Ladas, 1991, Recent developments in the oscillation of delay differnce equations, vol. 127, 321 Sharkovsky, 1993, vol. 250 Philos, 2004, An asymptotic result for some delay difference equations with continuous variable, Adv. Difference Equ., 1, 1 Shaikhet, 2004, About Lyapunov functionals construction for difference equations with continuous time, Appl. Math. Lett., 17, 985, 10.1016/j.aml.2003.06.011 Shaikhet, 2004, Construction of Lyapunov functionals for stochastic difference equations with continuous time, Math. Comput. Simulation, 66, 509, 10.1016/j.matcom.2004.03.006 Romanenko, 1998, Attractors of continuous difference equations, Comput. Math. Appl., 36, 377, 10.1016/S0898-1221(98)80038-2 Deng, 2003, A note on oscillation of second-order nonlinear difference equation with continuous variable, J. Math. Anal. Appl., 280, 188, 10.1016/S0022-247X(03)00068-4 Wu, 2004, Oscillation criteria for a class of neutral difference equations with continuous variable, J. Math. Anal. Appl., 290, 316, 10.1016/j.jmaa.2003.09.065 Zhang, 2001, Oscillations of a class of difference equations with continuous arguments, Appl. Math. Lett., 14, 557, 10.1016/S0893-9659(00)00194-4 Domshlak, 1993, Oscillatory properties of linear difference equations with continuous time, Differential Equations Dynam. Systems, 1, 311 Ladas, 1992, Necessary and sufficient conditions for the oscillation of difference equations, Panamer. Math. J., 2, 17 Shen, 2000, Comparison and oscillation results for difference equations with continuous variable, Indian J. Pure Appl. Math., 31, 1633 Yan, 1999, Oscillation for system of delay difference equations, J. Math. Anal. Appl., 230, 223, 10.1006/jmaa.1998.6195 Bainov, 1989 Gopalsamy, 1989, On delay differential equations with impulses, J. Math. Anal. Appl., 139, 110, 10.1016/0022-247X(89)90232-1 Peng, 2002, Oscillation theorems of second-order nonlinear neutral delay difference equations with impulses, Comput. Math. Appl., 44, 741, 10.1016/S0898-1221(02)00187-6 Wei, 2006, Oscillation of solutions of impulsive neutral difference equations with continuous variable, Int. J. Math. Math. Sci., 1, 10.1155/IJMMS/2006/34232 Zhang, 2002, On a linear delay difference equation with impulses, Ann. Differential Equations, 18, 197 He, 2004, Monotone iterative technique for first order impulsive difference equations with periodic boundary conditions, Appl. Math. Comput., 156, 605, 10.1016/j.amc.2003.08.013 Abdullin, 2000, Stability of nonlinear difference equations with pulse actions: A comparison method, Automat. Remote Control, Part 1, 61, 1796 Zhu, 2006, Global exponential stability of impulsive delay difference equation, Appl. Math. Comput., 181, 65, 10.1016/j.amc.2006.01.015 Xu, 2001, Asymptotic behavior of nonlinear difference equations with delays, Comput. Math. Appl., 42, 393, 10.1016/S0898-1221(01)00164-X Xu, 2003, Invariant and attracting sets of Volterra difference equations with delays, Comput. Math. Appl., 45, 1311, 10.1016/S0898-1221(03)00104-4 Seifert, 1976, Positively invariant closed sets for systems of delay differential equations, J. Differential Equations, 22, 292, 10.1016/0022-0396(76)90029-2 Xu, 2007, Attracting and invariant sets for a class of impulsive functional differential equations, J. Math. Anal. Appl., 329, 1036, 10.1016/j.jmaa.2006.05.072 Chu, 2003, A decomposition approach to analysis of competitive–cooperative neural networks with delay, Phys. Lett. A, 312, 339, 10.1016/S0375-9601(03)00692-3 Lasalle, 1976