Opuscula Math. 38, no. 4 (2018), 557-571

Opuscula Mathematica

Linear Sturm-Liouville problems with Riemann-Stieltjes integral boundary conditions

Qingkai Kong
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.

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  • Qingkai Kong
  • Northern Illinois University, Department of Mathematics, DeKalb, IL 60115, USA
  • Thomas E. St. George
  • Carroll University, Department of Mathematics, Waukesha, WI 53186, USA
  • Communicated by P.A. Cojuhari.
  • Received: 2017-07-20.
  • Accepted: 2017-08-08.
  • Published online: 2018-04-11.
Opuscula Mathematica - cover

Cite this article as:
Qingkai Kong, Thomas E. St. George, Linear Sturm-Liouville problems with Riemann-Stieltjes integral boundary conditions, Opuscula Math. 38, no. 4 (2018), 557-571, https://doi.org/10.7494/OpMath.2018.38.4.557

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