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References
N. CHAFEE: A bifurcation problem for a functional differential Equation of finitely retarded type. Journal of Mathematical Analysis and Applications 35.2. (1971), 312–349.
S.N. CHOW: Existence of periodic solutions of autonomous functional differential equations. Journal of differential equations. 15 (1974), 350–378.
S.N. CHOW-J. MALLET-PARET: Integral Averaging and bifurcation. Journal of Diff. Equat. vol. 26, No 7. Oct. 77.
B.D. COLEMAN-G.H. RENNINGER: Periodic solutions of certain nonlinear functional equation. Istituto Lombardo. Accad. Sci. Lett. Rend. A. 109 (1975), 91–111.
R.B. GRAFTON: A periodicity theorem for autonomous functional differential equations. Archiv. for rational mechanics and analysis. 65.1. (1977), 87–95.
D. GREEN Jr.: Periodic solutions of functional differential equations with applications to epidemic models.
K.P. HADELER-J. TOMIUK: Periodic solutions of differential difference equations. Archiv. for rational mechanics and analysis. 65.1. (1977), 87–95.
J.K. HALE: Theory of functional differential equations. Applied Mathematical sciences. V3. Springer Verlag. New-York (1971–1977).
J.K. HALE-C. PERELLO: The neighbourhood of a singular point of functional differential equations. Contribution differential equations. 3. (1964).
A.F. IZE: Asymptotic behavior and stability of neutral functional differential equations. Workshop on boundary value problems for ordinary differential equations and applications. Trieste (1977).
J.L. KAPLAN-A.J. YORKE: On nonlinear differential delay equations x′ (t) = − f(x(t),x(t-ω)). Journal of differential equations. 23.2. (1977), 293–314.
A. LEUNG: Periodic solutions for a prey-predator differential delay equations. Journal of differential equations. 26. (1977), 391–403.
J.C. LILLO: Oscillatory solutions of the equation y′ (x) = m(x)y(x-n(x)). Journal of differential equations. 6. (1969), 1–35.
R.D. NUSSBAUM: Periodic solutions of some nonlinear autonomous functional differential equations. Annali di Matematica. 4. 51. (1974), 263.
C. PERELLO: A note on periodic solutions of nonlinear differential equations with time lag. In Differential Equations and Dynamical Systems. 185–187. Academic Press, 1967. M.R. 36, 2896.
P. VIDAL-J.F. DENES: On phenomenia in ionized gases. IX Conférence internationale. Bucarest (1969) et thèse Toulouse (1971).
H.O. WALTHER: Existence of a non constant periodic solution of a nonlinear autonomous functional differential equation representing the growth of a single species population. Journal Mathematical Biosciences 1, (1975), 227–240.
O. ARINO-P. SEGUIER: Solutions périodiques d'équations à retard, critères de non existence (à paraître).
Oscillations autour d'un point stationnaire; conditions suffisantes de non existence. C.R. Acad. Sc. Paris. T. 284, (1977). A-145.
P. SEGUIER: Comportements de solutions d'équations différentielles à argument retardé (thèse 3ème cycle. Pau 1975). C.R. Acad. Sc. Paris 281, (1975), A-843.
A.M. ZVERKIN-G.A. KAMENSKII-S.B. NORKIN-L.E. EL'SGOL'TZ: Differential equations with retarded arguments, Uspchi Mat. Nauk. 17 (1962). 77–164. (article de synthèse).
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Arino, O., Séguier, P. (1979). Existence of oscillating solutions for certain differential equations with delay. In: Peitgen, HO., Walther, HO. (eds) Functional Differential Equations and Approximation of Fixed Points. Lecture Notes in Mathematics, vol 730. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064310
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DOI: https://doi.org/10.1007/BFb0064310
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