On boundary value problems which have spectral parameters in boundary conditions

Boundary value problems which have spectral parameter in boundary conditions are encountered while solving physics problems and until now various properties of this kind of problems are examined in several studies.In this thesis two types of problems which have spectral parameters in boundary conditions are handled. Firstly, the spectrum of second order boundary value problem with matrix coefficients, which has spectral parameter in boundary condition, is examined and expansion formulas according to eigenfunctions are obtained. Besides it is shown that spectral function and resolvent of self adjoint operator which is defined by this boundary value problem in a subspace are integral operators with matrix kernal. Second, discontinuous boundary value problem with retarded argument which has spectral parameter in boundary conditions and transmission conditions in discontinuity is examined, the asymptotic expressions of eigenvalues and eigenfunctions of this boundary value problem are obtained.