Opuscula Math. 38, no. 4 (2018), 557-571
Linear Sturm-Liouville problems with Riemann-Stieltjes integral boundary conditions
Thomas E. St. George
Abstract. We study second-order linear Sturm-Liouville problems involving general homogeneous linear Riemann-Stieltjes integral boundary conditions. Conditions are obtained for the existence of a sequence of positive eigenvalues with consecutive zero counts of the eigenfunctions. Additionally, we find interlacing relationships between the eigenvalues of such Sturm-Liouville problems and those of Sturm-Liouville problems with certain two-point separated boundary conditions.
Keywords: nodal solutions, integral boundary value problems, Sturm-Liouville problems, eigenvalues, matching method.
Mathematics Subject Classification: 34B10, 34B15.