Asymptotic behavior of solutions to the Dirac system with respect to a spectral parameter

We consider the Dirac system of ordinary differential equations \[ Y'(x) + {bmatrix} 0 & σ_1(x) \\ σ_2(x) & 0 {bmatrix} Y(x) = iμ{bmatrix} 1 & 0 \\ 0 & -1 {bmatrix} Y(x), Y(x) = {bmatrix} y_1(x) \\ y_2(x) {bmatrix}, \] where x ∈ [0,1], μ∈ C is a spectral parameter, and σⱼ ∈ Lᵖ[0,1], $j = 1,2,$ for p ∈ [1,2). We study the asymptotic behavior of the system's fundamental solutions as |μ| → ∞ in the half-plane Im μ> -r, where r ≥ 0 is fixed, and obtain detailed asymptotic formulas. As an application, we derive new results on the half-plane asymptotics of fundamental solutions to Sturm--Liouville equations with singular potentials.