%0 Journal Article %T The Uniqueness Theorem for the Solutions of Dual Equations of Sturm-Liouville Problems with Singular Points and Turning Points %J Sahand Communications in Mathematical Analysis %I University of Maragheh %Z 2322-5807 %A Mosazadeh, Seyfollah %D 2019 %\ 02/01/2019 %V 13 %N 1 %P 51-65 %! The Uniqueness Theorem for the Solutions of Dual Equations of Sturm-Liouville Problems with Singular Points and Turning Points %K Sturm-Liouville equation %K Singular points %K Turning points %K Dual equations %R 10.22130/scma.2018.73451.302 %X 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. %U https://scma.maragheh.ac.ir/article_34300_558e5017059030a2a631d70b10382c96.pdf