Third-order boundary value transmission problems

Abstract

In this paper, we consider some third-order operators with transmission conditions. In particular, it is shownthat such operators are formally symmetric in the corresponding Hilbert spaces and we introduce the resolvent operatorsassociated with the differential operators. After showing that the eigenvalues of the problems are real and discrete weintroduce some ordinary and Frechet derivatives of the eigenvalues with respect to some elements of data.