G.A.Kamenskii

The functional-differential equations of the type u'(x, t)=f (x, t, u_xt ) are called the it mixed functional-differential equations (MFDE). Here f is a functional of u_xt , depending on x and t as parameters.This equation is a generalization of mixed difference-differential equations, integro-differential of Barbashin type and other types of equations. The paper is a review containing following topics: the general theory of MFDE – problems of existence, uniqueness, smoothness of solutions of initial value and boundary value problem for different types of MFDE; the theory of linear MFDE; the theory of peroidic solutions of MFDE; the calculus of variations for nonlocal functionals.