Theoretical analysis for blow-up behaviors of differential equations with piecewise constant arguments

Abstract

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.