Stability of periodic solutions of first-order difference equations lying between lower and upper solutions (Q2495062)

The authors employ the method of upper and lower solutions to consider the existence and stability of periodic solutions of the first-order difference equation \[ u(n+1)=u(n)+f(n,u(n)),\quad n\in I_N=\{0,\dots,N-1\}, \] where \(f\) is a continuous function that is \(N\)-periodic in \(n\) and such that \(x\mapsto x+f(n,x)\) is strictly increasing for every \(n\in I_N.\) Several examples are given.