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