Existence of multiple positive periodic solutions for nonlinear functional difference equations
The authors consider the nonlinear delay difference equation \(x_{n+1}=a_nx_n+\lambda h_nf(x_{n-\tau(n)})\) where \(a_n\) \(h_n\) and \(\tau _{(n)}\) are positive periodic functions of period \(T\geq 1,\) \(\lambda >0\) and \(0<a_{n}<1.\) By using the fixed point theorem on the cone they establish some new sufficient conditions for existence of periodic solutions. The results give an affirmative answer to the question posed by \textit{Y. N. Raffoul} [Electron. J. Differ. Equ. 2003, Paper No. 102, 7 p., electronic only (2003; Zbl 1054.34115)].
scientific article; zbMATH DE number 2162016