On the resolvent of singular q-Sturm-Liouville operators

Abstract

In this paper, we investigate the resolvent operator of the singular q-Sturm-Liouville problem de…ned aswith the boundary conditionwhere 2 C, r is a real-valued function de…ned on [0; 1), continuous at zero and r 2 L 1 q;loc [0; 1). We give a representation for the resolvent operator and investigate some properties of this operator. Furthermore, we obtain a formula for the Titchmarsh-Weyl function of the singular q-Sturm-Liouville problem.