Maximum principles and boundary value problems for FDEs

The maximum principles present one of the classical parts in the quaUtative theory of ordinary and partial differential equations. Although assertions about the maximum principles for functional differential equations can be interpreted in a corresponding sense as analogs of corresponding classical ones in the case of ordinary differential equations, they do not imply important corollaries, reached on the basis of finite dimensional fundamental systems. For example, residts associated with the maximum principles in contrast with the cases of ordinary and even partial differential equations do not add so much in problems of existence and uniqueness. In this paper we obtain the maximum principles for functional differential equations and on this basis new residts on existence and uniqueness of solutions for various boundary value problems are proposed.