Add to ORKGThe paper is the investigation in the field of boundary-value problems for differential partial equations of elliptic type and is aimed at the consideration of a problem about the solution uniqueness and existence of elliptic equations of the second order in unbounded regions. The obtaining of the solution asymptotics in the infinity is also the aim of the paper. As a result the dimensionality of an operator nucleus with various weight functions has been calculated. The asymptotics on infinity of solutions with the finite Dirichlet's integral has been investigated. Existence and uniqueness theorems of external boundary-value problems of Dirichlet and Neumann in some functional spaces have been provedAvailable from VNTIC / VNTIC - Scientific...