Nonlocal Problem with Multipoint Perturbations of the Birkhoff Strongly Regular Boundary Conditions for an Even-Order Differential Operator

Abstract

We study spectral properties of a nonself-adjoint problem for a (2n ) th order operator of differentiation with nonlocal conditions representing multipoint perturbations of the Birkhoff strongly regular selfadjoint conditions. We establish sufficient conditions under which the system of eigenfunctions is complete and, under certain additional assumptions, forms a Riesz basis. We construct a set of transformation operators, each element of which maps the system of eigenfunctions of the unperturbed problem into the system of eigenfunctions of a certain isospectral problem. The cases of problems with Birkhoff regular and irregular two-point perturbations are analyzed. Finally, we establish conditions for the existence and uniqueness of the solution of the studied problem.