Differential Operator Equations with Interface Conditions in Modified Direct Sum Spaces

Abstract

We investigate a new type boundary value problem consisting of a
differential-operator equation, eigendependent boundary conditions
and two supplementary conditions so-called interface conditions. We
give a characterisation of some spectral properties of the
considered problem. Particularly, it is established such properties
as isomorphism and coerciveness, discreteness of the spectrum and
find asymptotic formulas for eigenvalues.