Generalized functional differential equations: existence and uniqueness of solutions

We study generalized nonlinear functional differential equations arising in various applications, for instance in the control theory, or if there is a need to incorporate impulsive and/or delay effects into the underlying system. The main result of the paper provides a general existence and uniqueness theorem for such equations, and we also give many illustrative examples. The proofs are based on the theory of generalized Volterra operators in the spaces of continuous and discontinuous functions