Almost periodic type solutions of differential equations with piecewise constant argument via almost periodic type sequences

Applied Mathematics Letters

Volumn 13, Issue 2, 2000, Pages 131-137

  Alonso, A I ^a   Hong, Jialin ^b   Obaya, R ^a  

^a UNIVERSITY OF VALLADOLID   (Spain)

^b INSTITUTE OF COMPUTATIONAL MATHEMATICS AND SCIENTIFIC ENGINEERING COMPUTING   (China)

Author keywords

Almost periodic functions; Almost periodic sequences; Asymptotically almost periodic functions; Asymptotically almost periodic sequences; Pseudo almost periodic functions; Pseudo almost periodic sequences

Indexed keywords

EID: 0008359440     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-9659(99)00176-7     Document Type: Article

References (16)

1. A.R. Aftabizadeh, J. Wiener and J.M. Xu, Oscillatory and periodic solutions of delay differential equations with piecewise constant argument, Proc. Amer. Math. Soc. 99, 673-679 (1987).
2. K.L. Cooke and J. Wiener, A survey of differential equations with piecewise constant argument, In Lecture Notes in Mathematics, Volume 1475, pp. 1-15, Springer-Verlag, Berlin, (1991).
3. J. Wiener, Generalized Solutions of Functional Differential Equations, World Scientific, (1993).
4. S. Busenberg and K.L. Cooke, Models of vertically transmitted diseases with sequential-continuous dynamics, In Nonlinear Phenomena in Mathematical Sciences, (Edited by V. Lakshmikantham), pp. 179-187, Academic Press, New York, (1982).
5. G.H. Meisters, On almost periodic solutions of a class of differential equations, Proc. Amer. Math. Soc. 10, 113-119 (1959).
6. Z. Opial, Sur les solutions presque-periodiques d'une classe d'equations differentielles, Ann. Polon. Math. 9, 157-181 (1960/61).
7. A.M. Fink, Almost periodic differential equations, In Lecture Notes in Mathematics, Volume 377, Springer-Verlag, Berlin, (1974).
8. B. Basit and C. Zhang, New almost periodic type functions and solutions of differential equations, Can. J. Math. 48 (6), 1138-1153 (1996).
9. C. Zhang, Pseudo almost-periodic solutions of some differential equations, J. Math. Anal. Appl. 181, 62-76 (1994).
10. C. Zhang, Integration of vector-valued pseudo-almost periodic functions, Proc. Amer. Math. Soc. 121, 167-174 (1994).
11. E. Ait Dads and O. Arino, Exponential dichotomy and existence of pseudo almost periodic solutions of some differential equations, Nonlinear Analysis, TMA 27 (4), 369-386 (1996).
12. E. Ait Dads, K. Ezzinbi and O. Arino, Pseudo almost periodic solutions for some differential equations in a Banach space, Nonlinear Analysis, TMA 28 (7), 1141-1155 (1997).
13. J. Hong, R. Obaya and A. Sanz, Almost periodic type solutions of some differential equations with piecewise constant arguments, Nonlinear Analysis, TMA (to appear).
14. R. Yuan and J. Hong, The existence of almost periodic solutions for a class of differential equations with piecewise constant argument, Nonlinear Analysis, TMA 28 (8), 1439-1450 (1997).
15. J. Hong and C. Núñez, On the almost periodic type difference equations, Mathl. Comput. Modelling 28 (12), 21-31 (1998).
16. L.A.V. Carvalho and K.L. Cooke, A nonlinear equation with piecewise continuous argument, Differential and Integral Equations (1), 359-367 (1988).