SAMARSKII-IONKIN TYPE NONLOCAL BOUNDARY VALUE PROBLEMS FOR A THREE-DIMENSIONAL EQUATION OF MIXED TYPE WITH TWO SINGULAR COEFFICIENTS

Abstract

Four nonlocal boundary value problems for a three-dimensional equation of mixed type with
two singular coefficients in an unbounded parallelepiped are investigated.. Unlike the earlier periodic
problem [1], the matching conditions in x are here of non-self-adjoint (Samarskii–Ionkin) type. The Fourier
method is used to construct, for each problem, a system of eigen- and associated functions; biorthogonality
with the corresponding adjoint system is proved, the resonant ODE system for the Fourier coefficients is
derived and solved explicitly by differentiating the Macdonald function with respect to the spectral
parameter, and uniqueness and existence theorems for a regular solution are established.