This paper considers a boundary value problem for the equation in some conical domains , where , , is a homogeneous polynomial of degree with real coefficients, and . An essential restriction on the domain is the following condition: the boundary contains no rays parallel to the -axis. The first part of the paper studies, for a wide class of domains , the asymptotics of a fundamental solution and the solution of a boundary value problem subject to the condition that the right-hand side and the boundary data tend rapidly to zero at infinity. In §3, for a specific domain and , a more involved case is examined, in which the right-hand side and the boundary data are unbounded.Bibliography: 13 titles.