Abstract:
Let $P$ be a differential operator of the form
$$
P=-\sum_{i,j=1}^n\frac\partial{\partial x_i}\biggl(a_{ij}(x)\varphi(x)\frac\partial{\partial x_j}\biggr)+a_0(x)
$$
in the domain $G\subseteq\mathbf R^n$ which has smooth boundary.
The asymptotic distribution of the eigenvalues of this operator is studied
in this paper. Under certain conditions on $\varphi(x)$ and $a_{ij}(x)$, lower
and upper estimates for the number of eigenvalues of $P$ are obtained.
Bibliography: 2 titles.
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