Spectral Analysis of Integro–Differential Equations in Viscoelasticity Theory

Abstract

We study spectral properties of boundary value problems for integro-differential equations in viscoelasticity theory. The sum of N exponential functions with negative exponents is taken for the convolution kernel. We prove that the spectrum of the boundary value problem is the union of N sequences of real numbers and two sequences all elements, except for finitely many ones, are not real. In particular, we obtain conditions under which these two sequences contains no real numbers. Bibliography: 8 titles.