Boundary eigenvalue problems for differential equations Nη = λPη with λ-polynomial boundary conditions

The present paper deals with the spectral properties of boundary eigenvalue problems for differential equations of the form N eta = lambdaP eta 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 greater than or equal to 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 lambda -independent boundary conditions. An application to a problem from elasticity theory is given. (C) 2001 Academic Press.