Extremal solutions and Green's functions of higher order periodic boundary value problems in time scales. (Q1426978)

The author develops a monotone iterative method in the presence of lower and upper solutions for the problem \[ u^{\Delta^n}(t)+\sum_{j=1}^{n-1}M_j u^{\Delta^j}(t)=f(t,u(t)), \quad t\in [a,b]=T^{\kappa^n} \] \[ u^{\Delta^i}(a)=u^{\Delta^i}(\sigma(b)), \quad i=0,1,\dots,n-1. \] Sufficient conditions are obtained on \(f\) to guarantee the existence and approximation of a solution lying between a pair of ordered lower and upper solutions.