The present paper deals with a class of third-order differential operators with eigenparameter dependent boundary conditions. The continuity of eigenvalues concerning a given parameter is proved. Moreover, the derivative formulas of eigenvalues concerning the parameters, in particular, the eigenparameter dependent boundary condition matrix, are given.
In this paper, we consider a Sturm-Liouville problem with finite discontinuous points inside an interval and with abstract linear functionals in the boundary and transmission conditions. For such a problem, the properties such as isomorphism, Fredholmness, and coerciveness with respect to the spectral parameter are investigated.
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