A class of second-order differential operators with eigenparameter-dependent boundary and transmission conditions

摘要

In this study, we investigate a Sturm-Liouville type problem with eigenparameter-dependent boundary conditions and eigenparameter-dependent transmission conditions. By establishing a new self-adjoint operator A associated with the problem, we construct fundamental solutions and obtain asymptotic formulae for its eigenvalues and fundamental solutions. Also we investigate some properties of its spectrum.