On a second-order matrix differential operator

We consider the second-order matrix differential operator $$N = left( {begin{array}{*{20}c} { - frac{d}{{dx}}left( {p_0 frac{d}{{dx}}} right) + p_1 } r end{array} begin{array}{*{20}c} r { - frac{d}{{dx}}left( {q_0 frac{d}{{dx}}} right) + q_1 } end{array} } right)$$ determined by the expression Nφ, [0 ?x < ∞), where (phi = left( {begin{array}{*{20}c} U V end{array} } right)) . It has been proved that if p₀, q₀, p₁, q₁,r satisfy certain conditions, then N is in the limit point case at ∞. It has been also shown that certain differential operators in the Hilbert space L² of vectors, generated by the operator N, are symmetric and self-adjoint.