**MSC:**- 35B40 Asymptotic behavior of solutions
- 35J25 Boundary value problems for second-order, elliptic equations
- 35J55 Boundary value problems for elliptic systems

pencils generated by boundary value problems for the Lam\'{e} system

\begin{equation} \label{0.1}

\Delta U + \frac{1}{\gamma}\, \mbox{grad\,div}\, U = F

\end{equation}

in a cone ${\cal K}.$ Here $U=(U_1,U_2,U_3)$ denotes the displacement

vector and $\gamma$ is a positive constant which is related to the

Poisson ratio $\nu$ via the equality $\gamma=1-2\nu.$

The study of the spectrum of these operator pencils is of great importance

for the description of the behaviour of the solutions near conical points.

It is well-known (see e.g. \cite{kon-67}, \cite{maz/plam-78/1},

\cite{naz/plam-94}) that the solutions of elliptic boundary value

problems in a neighbourhood of a conical point $x^{(0)}$ asymptotically

behave like a linear combination of terms of the form