The positive periodic solutions to a class of periodic Lotka-Volterra-type systems with infinite delay
Here, the existence of positive periodic solutions to the following periodic Lotka-Volterra-type system with delays NEWLINE\[NEWLINE\frac{dx_i(t)}{dt}= x_i(t)(a_i(t)-b_i(t)x_i(t)-f_i(t, x_t)),\quad i= 1,2,\cdots,n,NEWLINE\]NEWLINE is studied, with \(t\in \mathbb{R}\), \(x(t)= (x_1(t), x_2(t), \dots, x_n(t))\in \mathbb{R}^n\), \(x_t\in C^n\) and \(x_t(s)= x(t+s)\). By using Schauder's fixed-point theorem, a general criterion for the existence of positive periodic solutions is obtained, and some main results in the references are improved and extended.
scientific article; zbMATH DE number 1656178