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Periodic solutions of a delayed, periodic logistic equation. (English) Zbl 1118.34327
Consider the delay differential equation $${dN(t)\over dt}= N(t)[a(t)- b(t) N^p(t-\sigma(t))- c(t) N^q(t-\tau(t))],\tag{$*$}$$ where $a$, $b$, $c$, $\tau$ are continuous $\omega$-periodic functions, $p$ and $q$ are positive constants. The author establishes the existence of a positive $\omega$-periodic solution of $(*)$ by using Mawhin’s continuation theorem.

34K13Periodic solutions of functional differential equations
92D25Population dynamics (general)
Full Text: DOI
[1] Li, Y.; Kuang, Y.: Periodic solutions of periodic delay Lotka-Volterra equations and systems. J. math. Anal. appl. 255, No. 1, 260-280 (2001) · Zbl 1024.34062
[2] Yan, J.; Feng, Q.: Global attractivity and oscillation in a nonlinear delay equation. Nonlinear anal. 43, No. 1, 101-108 (2001) · Zbl 0987.34065
[3] Gopalsamy, K.; Ladas, G.: On the oscillation and asymptotic behavior of $N(t)=N(t)$[a + bn (t - ${\tau}$) - cn2(t -${\tau}$)]. Quart. appl. Math. 48, No. 3, 433-440 (1990) · Zbl 0719.34118
[4] Lalli, B. S.; Zhang, B. G.: On a periodic delay population model. Quart. appl. Math. 52, No. 1, 35-42 (1994) · Zbl 0788.92022
[5] Pianka, E. R.: Evolutionary ecology. (1974)
[6] Freedman, H. I.; Wu, J.: Periodic solutions of single species models with periodic delay. SIAM J. Math. anal. 23, No. 3, 689-701 (1992) · Zbl 0764.92016
[7] Kuang, Y.: Delay differential equations with applications in population dynamics. (1993) · Zbl 0777.34002
[8] Gaines, R. E.; Mawhin, J. L.: Coincidence degree and nonlinear differential equations. (1977) · Zbl 0339.47031
[9] Deimling, K.: Nonlinear functional analysis. (1985) · Zbl 0559.47040