Existence of periodic solutions for a class of nonlinear discrete systems (Q2928962)

The authors consider the following discrete nonautonomous system with delays: NEWLINE\[NEWLINE x_i(n) =\sum_{k=n-r_i}^n f_i(k,x_1(k),\dots,x_m(k)),\;\;i=1,\dots,m, NEWLINE\]NEWLINE where \(r_i\) are positive integers, \(f_i\) are nonnegative \(T\)-periodic with respect to the first variable and continuous with respect to last \(m\) variables function, \(f_i(k,x_1,\dots,x_{i-1},0,x_{i-1},\dots,x_m)=0\), \(i=1,\dots,m\).NEWLINENEWLINEThree theorems on existence of nontrivial \(T\)-periodic solutions to the system are proved. Two illustrative examples are presented.