**Z. Kamont, S. Kozieł**

## First
Order Partial Functional Differential Equations with

Unbounded Delay

**abstract:**

The phase space for nonlinear hyperbolic functional differential equations with
unbounded delay is constructed. The set of axioms for generalized solutions of
initial problems is presented. A theorem on the existence and continuous
dependence upon initial data is given. The Cauchy problem is transformed into a
system of integral functional equations. The existence of solutions of this
system is proved by the method of successive approximations and by using
theorems on integral inequalities. Examples of phase spaces are given.