Singular Sturm-Liouville problems whose coefficients depend rationally on the eigenvalue parameter

Let -Domega((.), z)D + q be a differential operator in L-2(0, infinity) whose leading coefficient contains the eigenvalue parameter z. For the case that omega((.), z) has the particular form

omega(t, z) = p(t) + c(t)(2)/(z - r (t)), z is an element of C \ R,

and the coefficient functions satisfy certain local integrability conditions, it is shown that there is an analog for the usual limit-point/limit-circle classification. In the limit-point case mild sufficient conditions are given so that all but one of the Titchmarsh-Weyl coefficients belong to the so-called Kac subclass of Nevanlinna functions. An interpretation of the Titchmarsh-Weyl coefficients is given also in terms of an associated system of differential equations where the eigenvalue parameter appears linearly. (C) 2004 Elsevier Inc. All rights reserved.