Mediterranean Journal of Mathematics

, Volume 11, Issue 2, pp 447–462 | Cite as

Resolvent Operator and Self-Adjointness of Sturm–Liouville Operators with a Finite Number of Transmission Conditions

Article

Abstract

In this paper, we consider a Sturm–Liouville operator with eigenparameter-dependent boundary conditions and transmission conditions at a finite number of interior points. We introduce a Hilbert space formulation such that the problem under consideration can be interpreted as an eigenvalue problem for a suitable self-adjoint linear operator. We construct Green function of the problem and resolvent operator. We establish the self-adjointness of the discontinuous Sturm–Liouville operator.

Mathematical Subject Classification (1991)

34B24 34B27 47E05 

Keywords

Sturm–Liouville problems eigenparameter-dependent boundary conditions transmission conditions self-adjoint resolvent operator green function 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Department of MathematicsPayame Noor UniversityAharIran
  2. 2.Faculty of Mathematical SciencesUniversity of TabrizTabrizIran

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