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Existence of positive periodic solutions for a class of difference equations with several deviating arguments. (English) Zbl 1052.39008
The authors consider the general periodic logistic difference equation $$ \triangle x(t) = x(t)[a(t)-g(t,x(t-\tau_1(t)),\ldots,x(t-\tau_n(t)))] $$ where $t\in Z$ and $a$, $g(\cdot,x_1,\ldots,x_n)$, $\tau_i(\cdot)$ are $T$-periodic. Conditions are given for the existence of a positive $T$-periodic solution of the equation, using a continuation theorem from {\it R. E. Gaines} and {\it J. L. Mawhin} [Coincidence degree, and nonlinear differential equations (1977; Zbl 0339.47031)].

39A11Stability of difference equations (MSC2000)
39A12Discrete version of topics in analysis
Full Text: DOI
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