1$, $n\in \mathbb{N}$, $l>0$, and $a_i$, $0\leq i\leq l$ are $n\times n$ matrix functions with sufficiently smooth entries and $\det a_0(x)\neq 0$; $(H_p^l)^n:=(H_p^l(0,1))^n$ is a Sobolev space of $n$-vector functions. The domain $\mathcal{D}(A)$ is supposed to be given by general boundary conditions \begin{equation} U(\varphi):=U_0 \begin{pmatrix} \varphi(0)\\ \varphi'(0)\\ \vdots\\ \varphi^{(l-1)}(0) \end{pmatrix} +U_1\begin{pmatrix} \varphi(1)\\ \varphi'(1)\\ \vdots\\ \varphi^{(l-1)}(1) \end{pmatrix}=0 \label{e5.1} \end{equation} where $U_0$ and $U_1$ are $nl\times nl$ matrices. The operator $B: \mathcal{D}(B)\subset X_2\to X_1$ is defined on $\mathcal{D}(B)=\{\varphi \in (H_{p}^s)^m : \hat{U}\varphi=0\}$, as \[ \varphi \mapsto B\varphi(x)= \sum_{k=0}^s b_k(x)\varphi^{(s-k)}(x). \] where $X_2:=(L_p(0,1))^m$, $m\in \mathbb{N}$, $0\leq s\leq l$; $b_i$, $0\leq i\leq s$ are $n\times m$ matrix functions with sufficiently smooth entries. The system of boundary conditions $U^{*}(v)=0$ ($v\in H_{q}^s$ with $q={\frac{p}{p-1}}$) is the adjoint of the system \eqref{e5.1}. We take all boundary conditions of order $\leq s-1$ in the system of boundary conditions $U^{*}(v)=0$ and denote the corresponding subsystem of linear forms by $\hat U^{*}(\cdot)$. The domain $\mathcal{D}(B)$ is chosen, on the one hand, to satisfy the condition $\mathcal{D}(B^{*})\supset \mathcal{D}(A^{*})$ and, on the other hand, to be as large as possible in order to cover examples which are interesting in applications. The operator $C: \mathcal{D}(C)\subset X_1 \to X_2$ is defined on $\mathcal{D}(C)=\{\varphi \in (H_{p}^h)^n : U\varphi=0\}$, as \[ \varphi \mapsto C\varphi(x)= \sum_{k=0}^h c_k(x)\varphi^{(h-k)}(x), \] where $0\leq h\leq l$, $s+h=l$ and $c_i$, $0\leq i\leq h$ are $m\times n$ matrix functions with sufficiently smooth entries. The operator $D: X_2 \to X_2$ is defined as \[ \varphi \mapsto D\varphi(x)= d(x)\varphi(x), \] where $d$ is an $m\times m$ matrix function which is assumed to be measurable and essentially bounded (hence $D$ is a bounded operator on $X_2$). For more details we refer the reader to \cite{Atkinson}. The next proposition contains conditions that we need in the sequel. \begin{proposition} \label{prop5.1} With the above notation, we have the following: \begin{itemize} \item[(i)] \cite[Proposition 4.1]{Atkinson} $B$ is closable and the inclusion $\mathcal{D}(B^{*})\supset \mathcal{D}((A^{*})^{\frac{s}{l}})$ holds. \item[(ii)] \cite[Proposition 4.2]{Atkinson} $C$ is closable and $\mathcal{D}(\bar C)\supset \mathcal{ D}((A^{*})^{\frac{h}{l}})$ \item[(iii)] \cite[Theorem 4.3]{Atkinson} For $\mu\in\rho(A)$ the operator $D-C(A-\mu I)^{-1}B$ which is defined on $\mathcal{D}(B)$, admits a bounded closure $S(\mu)=S_0+K(\mu)$, where $S_0$ is the operator of multiplication by the function $d-c_0a_0^{-1}b_0$ and $K(\mu)$ a compact operator in $X_2$. \end{itemize} \end{proposition} \begin{theorem} \label{thm5.1} Let $L_0$ the operator defined as above and let $L$ denote the closure of $L_0$. Then \begin{equation} \sigma_{ei}(L)=\{ \lambda\in \mathbb{C}: \mathop{\rm ess\,inf}| \det [d(x)-c_0(x)a_0^{-1}(x)b_0(x)-\lambda I]|=0\}\quad i=1,\dots,6. \label{e5.2} \end{equation} Moreover, if the complement of this set is connected, then this complement coincides with the domain of finite meromorphy of the operator function $(L-\lambda I)^{-1}$. \end{theorem} \begin{proof} Using Theorem \ref{thm4.2} and Proposition \ref{prop5.1} (iii) we deduce that $\sigma_{ei}(L)=\sigma_{ei}(S_0)$, $i=1,\dots,6$ where $S_0$ is the operator of multiplication by the matrix function $d-c_0a_0^{-1}b_0$. On the other hand, it is shown in \cite{Hardt} that the spectrum of $S_0$ is purely continuous and is given by the expression on the right-hand side of \eqref{e5.2}. Now the result follows from Remark \ref{rmk2.4}. \end{proof} \begin{thebibliography}{00} \bibitem{Adam} J. A. Adam, \emph{Physics reports (Review section of Physics Letters)}, 142, 5, 263-356 (1986). \bibitem{Agmon} S. Agmon, A. 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