Existence of periodic solutions for a state dependent delay differential equation

Journal of Differential Equations

Volumn 165, Issue 1, 2000, Pages 61-95

  Magal, P ^a   Arino, O ^b  

^a UNIVERSITÉ DU HAVRE   (France)

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

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034691326     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1999.3759     Document Type: Article

References (13)

1. W. Alt, "Periodic solutions of some autonomous differential equations with variable time delay," Lecture Notes in Mathematics, Vol. 730, pp. 16-31, Springer-Verlag, New York/Berlin, 1979.
2. O. Arino, K. P. Hadeler, and M. L. Hbid, Existence of periodic solutions for delay differential equations with state dependent delay, J. Differential Equations 144, No. 2 (1998), 263-301.
3. F. Browder, A further generalization of the Schauder fixed point theorem, Duke Math. J. 32 (1965), 575-578.
4. J. K. Hale, "Functional Differential Equations," Springer-Verlag, New York/Berlin, 1977.
5. J. K. Hale and S. M. Verduyn Lunel, "Introduction to Functional Differential Equations," Springer-Verlag, New York/Berlin, 1993.
6. Y. Kuan and H. L. Smith, Slowly oscillating periodic solutions of autonomous state-dependent delay equations, Nonlinear Anal. Theory Methods Appl. 19, No. 9 (1992), 855-872.
7. Y. Kuan and H. L. Smith, Periodic solutions of differential delay equations with threshold-type delays, oscillations and dynamics in delay equations, Contemp. Math. 129 (1992).
8. P. Magal, "Contribution à l'Étude des Systèmes Dynamiques Dicrets Préservant un Cône et Application à des Modèles de Dynamiques de Population," Ph.D. thesis, Pau, France, 1996.
9. P. Magal and O. Arino, A Semi-ejective Fixed Point Theorem, working paper, 1998.
10. J. Mallet-Paret and R. Nussbaum, Boundary layer phenomena for differential delay with state-dependent time lags, Arch. Rational Mech. Anal. 120 (1992), 99-146.
11. J. Mallet-Paret, R. Nussbaum, and P. Paraskevopulos, Periodic solutions to functional differential equations with multiple state-dependent time lags, in "Topological Methods in Nonlinear Analysis," Vol. 3, pp. 101-162, J. Juliusz Schauder Center, 1994.
12. R. Nussbaum, Periodic solutions of some nonlinear autonomous functional differential equations, Ann. Math. Pure Appl. 10 (1974), 263-306.
13. R. Nussbaum, "Periodic solutions of nonlinear autonomous functional differential equations," Lecture Notes in Math., Vol. 730, pp. 283-325, Springer-Verlag, New York/Berlin, 1979.