Mixed problems for hyperbolic functional differential equations with unbounded delay

The phase space for nonlinear hyperbolic functional differential equations with unbounded delay is constructed. The set of axioms for generalized solutions of initial boundary value problems is presented. A theorem on the existence and continuous dependence upon initial boundary data is given. The mixed 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.