MMN-509
A class of $2n$th-order differential operator with eigenparameter-dependent boundary and transmission conditions
Abstract
In this paper, we investigate a class of $2n$th-order regular differential operator with eigenparameter-dependent boundary conditions and transmission conditions at an interior discontinuous point. By constructing a new linear operator $A$ associated with the problem, we prove that the operator $A$ is self-adjoint in a suitable Hilbert space $H$, and the eigenvalues of the problem coincide with those of $A$. In terms of basic solutions of differential equation, we show that the eigenvalues of this problem coincide with the zeros of the entire function $detPhi(1,lambda)$, and obtain that the operator $A$ has only point spectrum.
Vol. 14 (2013), No. 1, pp. 355-372
DOI: 10.18514/MMN.2013.509