Aiping Wang, Jiong Sun, Xiaoling Hao, Siqin Yao
In this paper, we investigate a class of Sturm-Liouville problems with eigenparameter- dependent boundary conditions and transmission conditions at an interior point. A self-adjoint linear operator A is defined in a suitable Hilbert space H such that the eigenvalues of such a problem coincide with those of A. We show that the operator A has only point spectrum, the eigenvalues of the problem are algebraically simple, and the eigenfunctions of A are complete in H.
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