Boundary eigenvalue problems for differential equations N eta = lambda P eta with lambda-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 c ompact interval with boundary conditions which depend on the spectral param eter polynomially. Here N as well as P are regular differential operators o f order n and p, respectively. with n > p greater than or equal to 0. The m ain results concern the completeness, minimality, and Riesz basis propertie s of the corresponding eigenfunctions and associated functions. They are ob tained after a suitable linearization of the problem and by means of a deta iled asymptotic analysis of the Green's function. The function spaces where the above properties hold are described by lambda -independent boundary co nditions. An application to a problem from elasticity theory is given. (C) 2001 Academic Press.