NONLOCAL PROBLEMS WITH GENERALIZED SAMARSKY-IONKIN CONDITION FOR SOME CLASSES OF NONSTATIONARY DIFFERENTIAL EQUATIONS

Abstract

In this paper, we study the solvability of boundary value problems that are nonlocal with respect to the spatial variable for one-dimensional parabolic equations, as well as for some equations of the Sobolev type. Existence and uniqueness theorems are proved regular solutions – namely, solutions having all the derivatives generalized in the sense of S.L. Sobolev entering the corresponding equation.