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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 $$u^{\Delta^n}(t)+\sum_{j=1}^{n-1}M_j u^{\Delta^j}(t)=f(t,u(t)), \quad t\in [a,b]=T^{\kappa^n}$$ $$u^{\Delta^i}(a)=u^{\Delta^i}(\sigma(b)), \quad i=0,1,\dots,n-1.$$ 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.

##### MSC:
 39A12 Discrete version of topics in analysis 34B27 Green functions 93C70 Time-scale analysis and singular perturbations 34B15 Nonlinear boundary value problems for ODE
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##### References:
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