Existence of Periodic Solutions for Delay Differential Equations with State Dependent Delay

Journal of Differential Equations

Volumn 144, Issue 2, 1998, Pages 263-301

  Arino, O ^a   Hadeler, K P ^b   Hbid, M L ^c  

^a UNIVERSITÉ DE PAU ET DES PAYS DE L'ADOUR   (France)

^b UNIVERSITY OF TÜBINGEN   (Germany)

^c CADI AYYAD UNIVERSITY   (Morocco)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000065650     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1997.3378     Document Type: Article

References (16)

1. Aiello W. G., Freedman H. I., Wu J. Analysis of a model representing stage-structured population growth with state-dependent time delay. SIAM J. Appl. Math. 52:1992;855-869.
2. O. Arino, M. L. Hbid, R. Bravo de la Parra, A mathematical model of growth of population of fish in the larval stage: Density-dependence effects, Math. Biosc.
3. Arino O., Chérif A. More on ordinary differential equations which yield periodic solutions of delay differential equations. J. Math. Anal. Appl. 180:1993;361-385.
4. Browder F. A further generalization of the Schauder fixed point theorem. Duke Math. J. 32:1965;575-578.
5. Chow S., Hale J. K. Periodic solutions of autonomous equations. J. Math. Anal. Appl. 66:1978;495-506.
6. Györi I., Ladas G. Oscillation Theory of Delay Differential Equations with Applications. 1991;Clarendon pressOxford Mathematical Monographs, Oxford.
7. Hadeler K. P., Tomiuk J. Periodic solutions of difference differential equations. Arch. Rat. Mech. Anal. 65:1977;87-95.
8. Hale J. K. Functional Differential Equations. 1977;Springer-Verlag, Berlin.
9. Hale J. K., Verduyn Lunel S. M. Introduction to Functional Differential Equations. 1993;Springer-Verlag, Berlin.
10. Kuang Y., Smith H. L. Periodic solutions of differential delay equations with threshold-type delays, Oscillations and Dynamics in Delay Equations. Contemp. Math. 129:1992;153-176.
11. P. Magal, A fixed point theorem for maps on cones with application to a population dynamics model.
12. Mallet-Paret J., Nussbaum R. Boundary layer phenomena for differential delay equations with state-dependent time lags. Arch. Rat. Mech. Anal. 120:1992;99-146.
13. Mallet-Paret J., Nussbaum R., Paraskevopulos P. Periodic solutions to functional differential equations with multiple state-dependent time lags, Topological Methods in Nonlinear Analysis. J. Juliusz Schauder Center. 3:1994;101-162.
14. Nussbaum R. Periodic solutions of some nonlinear autonomous functional differential equations. Ann. Math. Pure Appl. 10:1974;263-306.
15. Nussbaum R. Periodic solutions of nonlinear autonomous functional differential equations. Lecture Notes in Math. 730:1979;283-325.
16. Wright E. M. A nonlinear differential difference equation. J. Reine Angew. Math. 194:1955;66-87.