On the asymptotic distribution of the eigenvalues of degenerating elliptic equations of second order

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.
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