Abstract
We consider a discontinuous Sturm-Liouville equation together with eigenparameter dependent boundary conditions and two supplementary transmission conditions at the point of discontinuity. By modifying some techniques of [2], [11] and [14] we extend and generalize some approach and results of classic regular Sturm-Liouville problems to the similar problems with discontinuities. In particular, we introduce a special Hilbert space formulation such a way that the considered problem can be interpreted as an eigenvalue problem of suitable self-adjoint operator, then we construct the Green function and resolvent operator and derive an asymptotic formulas for eigenvalues and normalized eigenfunctions.
Citation
O. Sh. Mukhtarov. Mahir Kadakal. F. S. Muhtarov. "On discontinuous Sturm-Liouville problems with transmission conditions." J. Math. Kyoto Univ. 44 (4) 779 - 798, 2004. https://doi.org/10.1215/kjm/1250281698
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