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Theoretical analysis for blow-up behaviors of differential equations with piecewise constant arguments. (English) Zbl 1410.34184
Summary: In this paper, we discuss the blow-up behaviors of differential equations with piecewise constant arguments (EPCAs). Some fundamental results on the local existence and uniqueness of solutions of EPCAs are reviewed and some conditions are given under which the unique solution exists globally. Sufficient conditions for the finite blowup are presented and some examples illustrate that the blow-up behaviors of EPCAs are quite different from those of the corresponding ordinary differential equations.

MSC:
34K05 General theory of functional-differential equations
34K12 Growth, boundedness, comparison of solutions to functional-differential equations
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