Elliptic Functional Differential Equations with Degenerations

Abstract: This review is devoted to differential-difference equations with degeneration in a bounded domain Q(Formula presented.).Rn and applications (Kato conjecture, nonlocal boundary value problem). We consider differential-difference operators with degeneration of the second order and generalization to 2m-order and the case where differential-difference operator contains several degenerate difference operators with degeneration. Generalized solutions of such equations may not belong even to the Sobolev space W1_2(Q). © 2020, Pleiades Publishing, Ltd.