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Positive periodic solutions of a delayed model in population. (English) Zbl 1058.34088
The authors consider a generalization of some population growth model in the form of a logistic equation with a countable number of delayed terms. This generalization is due to the presence of nonconstant periodic delays and of a convolution term. The authors prove the existence of a positive periodic solution by using the coincidence degree argument.

34K13Periodic solutions of functional differential equations
92D25Population dynamics (general)
Full Text: DOI
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[2] Seifert, G.: On a delay-differential equation for single species population variations. Nonlinear analysis TMA 9, 1051-1059 (1987) · Zbl 0629.92019
[3] Lenhart, S. M.; Travis, C. C.: Global stability of a biological model with time delay. Proc. amer. Math. soc. 96, 75-78 (1986) · Zbl 0602.34044
[4] Kuang, Y.: Delay differential equations with applications in population dynamics. (1993) · Zbl 0777.34002
[5] Gyori, I.; Ladas, G.: Oscillation theory of delay differential equations. (1991)
[6] Yu, J. S.: Global attractivity of zero solution for a class of functions and its applications. Science in China (Series A) 26, 23-33 (1996)
[7] Zhang, G. B.; Gopalsamy, K.: Global attractivity and oscillations in a periodic delay-logistic equation. J. math. Anal. appl. 150, 274-283 (1990) · Zbl 0711.34090
[8] Gainer, R. E.; Mawhin, J. L.: Coincidence degree, and non-linear differential equations. (1977)