In this paper, we investigate the Sturm-Liouville operators with transmission conditions and eigenparameter-dependent boundary conditions. By means of studying the operator itself, we study properties of its eigenvalues, and obtain the necessary and sufficient conditions for λ is an eigenvalue. By constructing the Green's function of the new operator A, we prove the completeness of their eignfunctions.
GAO Pengfei,YAO Siqin,SUN Jiong. Sturm-Liouville Operators with Transmission Conditions and Eigenparameter-dependent Boundary Conditions[J]. Acta Mathematicae Applicatae Sinica, 2012, (1): 156-167.
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