Spectral Method in the Theory of Mixed Type Equations.

We use the spectral method for Gellerstedt problem for Lavrent’ev-Bitsadze equation in a half-strip with Frankl condition on the type change line of the equation. Also a problem from the theory of parabolic-hyperbolic equations with the spectral parameter in the boundary condition is considered. We regard the case of appearing of a multiple eigenvalue by the eigenfunction and the associated function from the root subspace and removing of one eigenfunction with simple eigenvalue. [ABSTRACT FROM AUTHOR]