LAUSR

We consider a spectral problem for an elliptic differential operator debined on \begin{document}$ \mathbb{R}^n $\end{document} and acting on the generalized Sobolev space \begin{document}$ W^{0, \chi}_p(\mathbb{R}^n) $\end{document} for \begin{document}$ 1 . We note that similar problems, but with \begin{document}$ \mathbb{R}^n $\end{document} replaced by either a bounded region in \begin{document}$ \mathbb{R}^n $\end{document} or by a closed manifold have been the subject of investigation by various authors. Then in this paper we establish, under the assumption of parameter-ellipticity, results pertaining to the existence and uniqueness of solutions of the spectral problem. Furthrermore, by utilizing the aforementioned results, we obain results pertaining to the spectral properties of the Banach space operator induced by the spectral problem.