Boundary Eigenvalue Problems for Differential Equations Nη=λPη with λ-Polynomial Boundary Conditions

Abstract

AbstractThe present paper deals with the spectral properties of boundary eigenvalue problems for differential equations of the form Nη=λPη on a compact interval with boundary conditions which depend on the spectral parameter polynomially. Here N as well as P are regular differential operators of order n and p, respectively, with n>p⩾0. The main results concern the completeness, minimality, and Riesz basis properties of the corresponding eigenfunctions and associated functions. They are obtained after a suitable linearization of the problem and by means of a detailed asymptotic analysis of the Green's function. The function spaces where the above properties hold are described by λ-independent boundary conditions. An application to a problem from elasticity theory is given