Coupled solutions and monotone iterative techniques for some nonlinear initial value problems on time scales.
The authors present the monotone iterative technique for nonlinear initial value problems, which consists in approximating the unique solution by lower and upper solutions. The well-known theory is generalized in two respects: 1) Various types of (dynamic) inequalities (with natural or coupled solutions) constitute the framework of the theory. 2) The set of the underlying independent variable, which is \(\mathbb R\) in the classical theory, is replaced by a general time scale, i.e., an arbitrary closed subset of \(\mathbb R\). So, also the difference equations case (\(\mathbb Z\) as a time scale) is covered. The authors also point out applications to the logistic equation of mathematical biology. Reviewer's remark: An error in step (iii) of the proof of Theorem 3.3 can be fixed.
scientific article; zbMATH DE number 1910217