Asymptotic Properties of Solutions of the Dirichlet Problem in the Half-Plane for Differential-Difference Elliptic Equations

The Dirichlet problem in the half-plane for elliptic equations containing, in addition to differential operators, the shift operator with respect to the variable parallel to the boundary of the domain is considered. The behavior of the solution as the variable orthogonal to the boundary of the domain increases unboundedly is studied.