Mediterranean Journal of Mathematics

, Volume 11, Issue 2, pp 447–462

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


DOI: 10.1007/s00009-013-0338-1

Cite this article as:
Dehghani, I. & Akbarfam, A.J. Mediterr. J. Math. (2014) 11: 447. doi:10.1007/s00009-013-0338-1


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)



Sturm–Liouville problemseigenparameter-dependent boundary conditionstransmission conditionsself-adjointresolvent operatorgreen function

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© Springer Basel 2013

Authors and Affiliations

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