Generalized Solutions of Nonlocal Elliptic Problems

An elliptic equation of order $2m$ with general nonlocal boundary-value conditions, in a plane bounded domain $G$ with piecewise smooth boundary, is considered. Generalized solutions belonging to the Sobolev space $W_2^m(G)$ are studied. The Fredholm property of the unbounded operator (corresponding to the elliptic equation) acting on $L_2(G)$, and defined for functions from the space $W_2^m(G)$ that satisfy homogeneous nonlocal conditions, is established.