Spectrum and spectral singularities of a quadratic pencil of a Schrodingeroperator with a general boundary condition

In this article we investigate the spectrum and the spectral singularities of the Quadratic Pencil of Schrodinger Operator L generated in L-2(R+) by t he differential expression t(y) = -y " + [q(x) + 2 lambda p(x) - lambda(2)] y, x is an element of R+ = [0, infinity) and the boundary condition [GRAPHICS] where p, q, and K are complex valued functions, p is continuously different iable on R+, K is an element of L-2(R+), and alpha, beta is an element of C , with \alpha\ + \beta\ not equal 0. Discussing the spectrum, we prove that L has a finite number of eigenvalues and spectral singularities with finit e multiplicities, if the conditions [GRAPHICS] Later we investigate the properties of the principal functions correspondin g to the spectral singularities. Moreover. some results about the spectrum oft are applied to non-selfadjoint Sturm-Liouville and Klein-Gordon s-wave operators. (C) 1999 Academic Press.