  In this work, we find the asymptotic formulas for the sum of the negative
eigenvalues smaller than $-\varepsilon$ $(\varepsilon >0)$ of a self-adjoint
operator $L$ which is defined by the following differential expression
$$\ell(y)=-(p(x)y'(x))'-Q(x)y(x)$$ with the boundary condition $y(0) = 0$ in
the space in the space $L_{2}(0,\infty ;H)$.
