REFERENCES
- S. M. Shah and J. Wiener ( 1983 ). Advanced differential equations with piecewise constant argument deviations . Internat. J. Math. Math. Sci. 6 : 671 – 703 .
- K. L. Cooke and J. Wiener ( 1984 ). Retarded differential equations with piecewise constant delays . J. Math. Anal. Appl. 99 : 265 – 297 .
- J. Wiener ( 1983 ). Differential equations with piecewise constant delays . In: V. Lakshmikantham Trends in the Theory and Practice of Nonlinear Differential Equations . New York : Marcel Dekker , pp. 547 – 552 .
- J. Wiener and K. L. Cooke ( 1989 ). Oscillations in systems of differential equations with piecewise constant argument . J. Math. Anal. Appl. 137 : 221 – 239 .
- Y. H. Xia , Z. K. Huang , and M. A. Han ( 2007 ). Existence of almost periodic solutions for forced perturbed systems with piecewise constant argument . J. Math. Anal. Appl. 333 : 798 – 816 .
- Y. Muroya ( 2008 ). New contractivity condition in a population model with piecewise constant arguments . J. Math. Anal. Appl. 346 : 65 – 81 .
- M. U. Akhmet ( 2007 ). On the reduction principle for differential equations with piecewise constant argument of generalized type . J. Math. Anal. Appl. 336 : 646 – 663 .
- J. Wiener ( 1993 ). Generalized Solutions of Functional Differential Equations . Singapore : World Scientific .
- Z. G. Luo and J. H. Shen ( 2003 ). New results on oscillation for delay differential equations with piecewise constant argument . Comput. Math. Appl. 45 : 1841 – 1848 .
- M. U. Akhmet ( 2008 ). Asymptotic behavior of solutions of differential equations with piecewise constant argument . Appl. Math. Lett. 21 : 951 – 956 .
- H. Li , Y. Muroya , and R. Yuan ( 2009 ). A sufficient condition for the global asymptotic stability of a class of logistic equations with piecewise constant delay . Nonlinear Anal. 10 : 244 – 253 .
- M. Z. Liu , S. F. Ma , and Z. W. Yang ( 2007 ). Stability analysis of Runge-Kutta methods for unbounded retarded differential equations with piecewise continuous arguments . Appl. Math. Comput. 191 : 57 – 66 .
- M. Z. Liu , M. H. Song , and Z. W. Yang ( 2004 ). Stability of Runge-Kutta methods in the numerical solution of equation u(t) = au(t) + a 0 u([t]) . J. Comput. Appl. Math. 166 : 361 – 370 .
- M. H. Song , Z. W. Yang , and M. Z. Liu ( 2005 ). Stability of θ-methods for advanced differential equations with piecewise continuous arguments . Comput. Math. Appl. 49 : 1295 – 1301 .
- M. Z. Liu , J. F. Gao , and Z. W. Yang ( 2007 ). Oscillation analysis of numerical solution in the θ-methods for equation x(t) + ax(t) + a 1 x([t − 1]) = 0 . Appl. Math. Comput. 186 : 566 – 578 .
- M. Z. Liu , J. F. Gao , and Z. W. Yang ( 2009 ). Preservation of oscillations of the Runge-Kutta method for equation x(t) + ax(t) + a 1 x([t − 1]) = 0 . Comput. Math. Appl. 58 : 1113 – 1125 .
- Q. Wang , Q. Y. Zhu , and M. Z. Liu ( 2011 ). Stability and oscillations of numerical solutions for differential equations with piecewise continuous arguments of alternately advanced and retarded type . J. Comput. Appl. Math. 235 : 1542 – 1552 .
- I. Györi and G. Ladas ( 1991 ). Oscillation Theory of Delay Equations: with Applications . Oxford , UK : Clarendon Press .
- Z. W. Yang , M. Z. Liu , and M. H. Song ( 2005 ). Stability of Runge-Kutta methods in the numerical solution of equation u′(t) = au(t) + a 0 u([t]) + a 1 u([t − 1]) . Appl. Math. Comput. 163 : 37 – 50 .