Almost periodic solutions of a class of singularly perturbed differential equations with piecewise constant argument

Nonlinear Analysis, Theory, Methods and Applications

Volumn 37, Issue 7, 1999, Pages 841-859

  Yuan, Rong ^a  

^a BEIJING NORMAL UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; PERTURBATION TECHNIQUES; PIECEWISE LINEAR TECHNIQUES; PROBLEM SOLVING; SET THEORY; THEOREM PROVING;

PIECEWISE CONSTANT ARGUMENTS; SINGULARLY PERTURBED DIFFERENTIAL EQUATIONS;

DIFFERENTIAL EQUATIONS;

EID: 0033196939     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(98)00076-5     Document Type: Article

References (20)

1. A.R. Aftabizadeh, J. Wiener, J.M. Xu, Oscillatory and periodic solutions of delay differential equations with piecewise constant argument, Proc. Amer. Math. Soc. 99 (1987) 673-679.
2. D.V. Anosov, On limit cycles in systems of differential equations with a small parameter in the highest derivative, Amer. Soc. Trans. 33(2) (1963) 233-275.
3. S. Busenberg, K.L. Cooke, Models of vertically transmitted diseases with sequential continuous dynamics, in: V. Lakshmikantham (Ed.), Nonlinear Phenomena in Mathematical Sciences, Academic Press, New York, 1982, pp. 179-187.
4. K.W. Chang, Almost periodic solutions of singularly perturbed systems of differential equations, J. Differential Equations 4 (1968) 300-307.
5. K.L. Cooke, J. Wiener, Retarded differential equations with piecewise constant delays, J. Math. Anal. Appl. 99 (1984) 265-297.
6. K.L. Cooke, J. Wiener, A survey of differential equations with piecewise continuous argument, Lecture Notes in Mathematics, vol. 1475, Springer, Berlin, 1991, pp. 1-15.
7. K.L. Cooke, J. Wiener, Neutral differential equations with piecewise constant arguments, Bollettino Unione Mathematica Italiana 7 (1987) 321-346.
8. A.M. Fink, Almost periodic differential equations, Lecture Notes in Mathematics, vol. 377, Springer, Berlin, 1974.
9. L. Flatto, N. Levinson, Periodic solutions of singularly perturbed systems, J. Rat. Mech. Anal. 4 (1955) 943-950.
10. J.K. Hale, G. Seifert, Bounded and almost periodic solutions of singularly perturbed equations, J. Math. Anal. Appl. 3 (1961) 18-24.
11. C.Y. He, Almost Periodic Differential Equations, Higher Education Press, Beijing, 1992 (in Chinese).
12. G.H. Meisters, On almost periodic solutions of a class of differential equations, Proc. Amer. Math. Soc. 10 (1959) 113-119.
13. G. Papaschinopoulos, Some results concerning a class of differential equations with piecewise constant arguments, Math. Nachr. 166 (1994) 193-206.
14. G. Papaschinopoulos, On asymptotic behavior of the solutions of a class of perturbed differential equations with piecewise constant argument, J. Math. Anal. Appl. 185 (1994) 490-500.
15. R.J. Sacker, G.R. Sell, Singularly perturbation and conditional stability, J. Math. Anal. Appl. 76 (1980) 406-431.
16. S.M. Shah, J. Wiener, Advanced differential equations with piecewise constant argument deviations, Internat. J. Math. Math. Soc. 6 (1983) 671-703.
17. H.L. Smith, On the existence and stability of bounded, almost periodic and periodic solutions of a singularly perturbed nonautonomous system, Differential Intel. Equations 8:8 (1995) 2125-2144.
18. J. Wiener, K.L. Cooke, Oscillations in systems of differential equations with piecewise constant arguments, J. Math. Anal. Appl. 137 (1989) 221-239.
19. J. Wiener, Generalized Solutions of Functional Differential Equations, World Scientific, Singapore, 1993.
20. R. Yuan, J. Hong, Almost periodic solutions of differential equations with piecewise constant argument, Analysis 16 (1996) 171-180.