Existence of eigenvalues of problem with shift for an equation of parabolic-hyperbolic type

Abstract

In the paper a spectral problem for an operator of parabolic - hyperbolic type of I kind with non - classical boundary conditions is considered. The problem is considered in a standard domain. The parabolic part of the space is a rectangle. And the hyperbolic part of the space coincides with a characteristic triangle. We consider a problem with the local boundary condition in the domain of parabolicity and with the boundary condition with displacement in the domain of hyperbolicity. We prove the strong solvability of considered problem. The main aim of the paper is the research of spectral properties of the problem. The existence of eigenvalues of the problem is proved.