The operator pencil generated by a boundary value problem

In this thesis, some spectral properties of a many-interval boundary value problem defined on three non-intersecting interval with transmission conditons and one of the boundary condition having an eigenvalue parameter are investigated. First of all, importance of the problem, its application areas and previous studies are mentioned. Then, basic definitions and theorems about our problem are given. In the main part of our thesis Hilbert space have been found of the appropriate for our problem, the necessary concepts and inequalities have been given, and the concept of generalized solutions in accordance with the eigenvalues has been defined. In addition, the analyzed problem is reduced to the operator pencil equation and some properties of this operator pencil are examined. Finally it has been shown that the generalized eigenfunctions form a Riesz basis on the appropriate Hilbert space and a lower limit is estimated for the eigenvalues by using Rayleigh-Ritz method.