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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

x(t)=x(t)[a(t)-g(t,x(t-τ 1 (t)),...,x(t-τ n (t)))]

where tZ and a, g(·,x 1 ,...,x n ), τ i (·) are T-periodic. Conditions are given for the existence of a positive T-periodic solution of the equation, using a continuation theorem from R. E. Gaines and J. L. Mawhin [Coincidence degree, and nonlinear differential equations (1977; Zbl 0339.47031)].

MSC:
39A11Stability of difference equations (MSC2000)
39A12Discrete version of topics in analysis