Asymptotics of the Solutions of the Sturm–Liouville Equation with Singular Coefficients

We obtain asymptotic representations as $\lambda \to \infty$ in the upper and lower half-planes for the solutions of the Sturm–Liouville equation
$$ -y''+p(x)y'+q(x)y= \lambda ^2 \rho(x)y, \qquad x\in [a,b] \subset \mathbb{R}, $$
under the condition that $q$ is a distribution of first-order singularity, $\rho$ is a positive absolutely continuous function, and $p$ belongs to the space $L_2[a,b]$.