×

A new almost-periodic type of solutions to second-order neutral delay differential equations with piecewise constant argument. (English) Zbl 0961.34062

From the author’s abstract: A definition of pseudo almost-periodic sequences is given and the existence of a pseudo almost-periodic sequence to difference equations is studied. Based on these, the existence of pseudo almost-periodic solutions to neutral delay differential equations with piecewise constant argument is investigated.
Reviewer: W.M.Oliva (Lisboa)

MSC:

34K14 Almost and pseudo-almost periodic solutions to functional-differential equations
34K40 Neutral functional-differential equations
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Zhang, C., Pseudo almost periodic solutions of some differential equations, J. Math. Anal. Appl., 1994, 181: 62. · Zbl 0796.34029
[2] Dads, E. A., Arino, O., Exponential dichotomy and existence of pseudo almost periodic solutions of some differential equations, Nonlinear Analysis, TMA, 1996, 27(4): 369. · Zbl 0855.34055
[3] Yuan, R., On the existence of almost periodic solutions of second order neutral delay differential equations with piecewise constant argument, Sci. in China, Ser. A, 1998, 41(3): 232. · Zbl 0908.34054
[4] Yuan, R., Pseudo almost periodic solutions of second order neutral delay differential equations with piecewise constant argument, to appear in Nonlinear Analysis, TMA.
[5] Papaschinopoulos, G., Schinas. J., Some results concerning second and third neutral delay differential equations with piece-wise constant argument, Czechoslovak Math., 1994, 44: 501. · Zbl 0817.34041
[6] Cooke, K. L., Wiener, J., A survey of differential equation with piecewise continuous argument, in Lecture Notes in Mathematics (eds. Busenberg S. Martelli, M.), Vol. 1475, Berlin: Springer-Verlag, 1991, 1–15. · Zbl 0737.34045
[7] Yuan, R., Hong, J., The existence of almost periodic solution for a class of differential equations with piecewise constant argument, Nonlinear Analysis, TMA, 1997, 28(8): 1439. · Zbl 0869.34038
[8] Yuan, R., Hong, J., Almost periodic solutions of differential equations with piecewise constant argument, Analysis, 1996, 16: 171. · Zbl 0855.34089
[9] Busenberg, S., Cooke, K. L., Models of vertically transmitted diseases with sequential continuous dynamics, in Nonlinear Phenomena in Mathematical Sciences (ed. Lakshmikantham, V.), New York: Academic F’ress, 1982, 179–187. · Zbl 0512.92018
[10] Cooke, K. L., Wiener, J., Retarded differential equations with piecewise constant delays, J. Math. Anal. Appl., 1984, (99): 265. · Zbl 0557.34059
[11] Shah, S. M., Wiener, J., Advanced differential equations with piecewise constant argument deviations, Internat. J. Math. Math. Soc., 1983, 62671. · Zbl 0534.34067
[12] Wiener, J., Generalized Solutions of Functional Differential Equations, Singapore: World Scientific, 1993. · Zbl 0874.34054
[13] Fink, A. M., Almost periodic differential equations, in Lecture Notes in Mathematics, Vol. 377, Berlin: Springer-Verlag, 1974. · Zbl 0325.34039
[14] Meisters, G. H., On almost periodic solutions of a clam of differential equations, Proc. Amer. Math. Soc., 1959, (10): 113. · Zbl 0092.30401
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.