On positive periodic solutions of functional difference equations with forcing term and applications

Consider the following non-autonomous first order functional difference equation @Dx(n)=a(n)x(n)-@lh(n)f(n,x(n),x(n-@t"1(n)),...,x(n-@t"m(n)))+r(n),n@?Z. It is shown that, under certain assumptions, there exist positive periodic solutions. Applications are given to illustrate the main results.