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Extremal solutions and Green’s functions of higher order periodic boundary value problems in time scales. (English) Zbl 1056.39018

The author develops a monotone iterative method in the presence of lower and upper solutions for the problem

u Δ n (t)+ j=1 n-1 M j u Δ j (t)=f(t,u(t)),t[a,b]=T κ n
u Δ i (a)=u Δ i (σ(b)),i=0,1,,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.

39A12Discrete version of topics in analysis
34B27Green functions
93C70Time-scale analysis and singular perturbations
34B15Nonlinear boundary value problems for ODE