The Uniqueness Theorem for the Solutions of Dual Equations of Sturm-Liouville Problems with Singular Points and Turning Points

In this paper, linear second-order differential equations of Sturm-Liouville type having a finite number of singularities and turning points in a finite interval are investigated. First, we obtain the dual equations associated with the Sturm-Liouville equation. Then, we prove the uniqueness theorem for the solutions of dual initial value problems