4.3. Fredholm Solvability of Nonlocal Problems 6

This is the second part of the paper (for the first part, see Russ. J. Math. Phys., vol. 10, no. 4, pp. 436–466; the numbering of the sections continues that of part one). We study elliptic equations of order 2m with nonlocal boundary-value conditions in plane bounded domains for the case in which the support of nonlocal terms can nontrivially intersect the boundary. We give necessary and sufficient conditions for nonlocal problems to have the Fredholm property in Sobolev spaces and in weighted spaces with small weight exponents, respectively. We also find the asymptotic behavior of solutions of nonlocal problems near the conjugation points on the boundary, where solutions can have power-law singularities. CONTENT