Existence and global attractivity of periodic solutions to some classes of difference equations

Abstract

Existence and global attractivity of periodic solutions to some subclasses of the following class of difference equations xn+1 = qnxn + f(n,xn, xn-1,..., xn-k), n ? N0, where k ? N0, (qn)n?N0 is a T-periodic sequence (T ? N), and f : N0 x Rk+1 ? R is a T-periodic function in the first variable, which for each n ? {0,1,..., T-1} is continuous in other variables, are studied.