Asymptotic behavior of solutions of the Dirac system with an integrable potential

Abstract

We consider the Dirac system on the interval $[0,1]$ with a spectral parameter $\mu\in\mathbb{C}$ and a complex-valued potential with entries from $L_p[0,1]$, where $1\leq p <2$. We study the asymptotic behavior of its solutions in a stripe $|{\rm Im}\,\mu|\le d$ for $\mu\to \infty$. These results allows us to obtain sharp asymptotic formulas for eigenvalues and eigenfunctions of Sturm--Liouville operators associated with the aforementioned Dirac system.