Existence of positive periodic solutions for a class of difference equations with several deviating arguments
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 \textit{R. E. Gaines} and \textit{J. L. Mawhin} [Coincidence degree, and nonlinear differential equations (1977; Zbl 0339.47031)].
scientific article; zbMATH DE number 2082235
scientific article