A review of the theory of mixed functional-differential equations
G.A.Kamenskii
The functional-differential equations of the type u'(x, t)=f (x, t, uxt ) are called the it mixed functional-differential equations (MFDE). Here f is a functional of uxt , 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.
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