Open Access Research

Inverse problem for a class of Sturm-Liouville operator with spectral parameter in boundary condition

Khanlar R Mamedov* and F Ayca Cetinkaya

Author Affiliations

Department of Mathematics, Science and Letters Faculty, Mersin University, Mersin, 33343, Turkey

For all author emails, please log on.

Boundary Value Problems 2013, 2013:183  doi:10.1186/1687-2770-2013-183

Published: 14 August 2013

Abstract

This work aims to examine a Sturm-Liouville operator with a piece-wise continuous coefficient and a spectral parameter in boundary condition. The orthogonality of the eigenfunctions, realness and simplicity of the eigenvalues are investigated. The asymptotic formula of the eigenvalues is found, and the resolvent operator is constructed. It is shown that the eigenfunctions form a complete system and the expansion formula with respect to eigenfunctions is obtained. Also, the evolution of the Weyl solution and Weyl function is discussed. Uniqueness theorems for the solution of the inverse problem with Weyl function and spectral data are proved.

MSC: 34L10, 34L40, 34A55.

Keywords:
Sturm-Liouville operator; expansion formula; inverse problem; Weyl function