Fundamental Solutions of Two Degenerated Elliptic Equations and Solutions of Boundary Value Problems in Infinite Area

In the domain D = {(x,y,z) : 0 < x, -infinity < y < +infinity < z < +infinity} it is considered elliptic type equation with singular coefficient L-alpha(lambda) (u) equivalent to u(xx) + u(yy) +uzz + 2 alpha/xu(x) + lambda(2)u = 0, 0 < 2 alpha < 1, lambda = lambda(1) + i lambda(2), lambda(1), lambda(2) is an element of R. Fundamental solutions that express through confluent hypergeometric functions of Kummer H-3 (a, b; c; x, y) from two arguments were found for the given equation. By means of expansion confluent hypergeometric functions of Kummer it is proved, the constructed solutions have a singularity of the order 1/r at r -> 0. Further, in case of when lambda(2) = -mu(2) for the certain equation by means of found fundamental solutions, boundary value problems are solved in the domain D.