On a nonlocal problem of Bitsadze{Samarskii type for an elliptic equation with degeneration

In this paper, a nonlocal problem of the BitsadzeSamarskii type is studied for a degenerate elliptic equation in a vertical half-strip Ω = f(x; y) : 0 < x < 1; y > 0g. The problem connects the value of the sought function on the right boundary of the domain with its value at an interior point of the same domain. Under certain conditions on the given functions, theorems on the existence and uniqueness of the solution are proved. The uniqueness of the solution is proved using the maximum principle, while the existence of a solution is established by methods of separation of variables and integral equations.