Estimates of the discrete spectrum of a linear operator pencil

Based on the direct methods of the perturbation theory, sufficient conditions for the finiteness of the discrete spectrum of linear pencils of the form L(λ) = B − λA, where A and B are bounded self-adjoint operators, are established. An estimate formula for the discrete spectrum is also presented. As applications, we study the spectrum of the characteristic equation of radiation energy transfer. © 2006 Elsevier Inc. All rights reserved