  In this paper we introduce a general type of differential equations with
piecewise constant argument (EPCAG), and consider the problem of backward
continuation of solutions. We establish the existence of global integral
manifolds of quasilinear EPCAG, consisting of infinitely back continued
solutions, while the solutions starting outside the invariant sets may not be
back continued. The smoothness of the manifolds is investigated. The existence
of bounded and periodic solutions is considered. A new technique of
investigation of equations with piecewise argument, based on an integral
representation formula, is proposed.

Dynamical Systems