An extension of Mercer's theorem to a class of non-symmetric integral equations

Abstract

In this paper it is shown that certain properties of selfadjoint boundary value problems with positive eigenvalues, like the countability of the discrete eigenvalues and the expand-ability of the problem's Green function, are presevred if the problem is perturbed and becomes non-selfadjoint through an additional term involving a positive, continuously varying parameter. This is so, if the parameter remains small enough and does not transgress the so called stability domain of the problem.