Nonlocal Multipoint Problem for Partial Differential Equations of Even Order with Constant Coefficients

Abstract

For a partial differential equation of even order with constant coefficients, in a bounded domain G, we study a problem with boundary conditions in the form of multipoint perturbations of the Neumann conditions by using the Fourier method. The eigenvalues and eigenfunctions of the operator L of the multipoint problem are determined. We establish the conditions of completeness of the system of eigenfunctions V(L) of the operator L in the space L2 (G). In the case of elliptic equation, we establish the conditions under which the system V(L) is a Riesz basis in the space L2 (G). We construct the solution of an inhomogeneous problem with homogeneous multipoint conditions in the form of a Fourier series with respect to the system of eigenfunctions and establish conditions for its existence and uniqueness.