AbstractWe consider the Dirac system on the interval [0, 1] with a spectral parameter $$\mu \in {\mathbb {C}}$$
μ
∈
C
and a complex-valued potential with entries from $$L_p[0,1]$$
L
p
[
0
,
1
]
, where $$1\le p$$
1
≤
p
. We study the asymptotic behavior of its solutions in a strip $$|\mathrm{Im}\,\mu |\le d$$
|
Im
μ
|
≤
d
for $$\mu \rightarrow \infty $$
μ
→
∞
. These results allow us to obtain sharp asymptotic formulas for eigenvalues and eigenfunctions of Sturm–Liouville operators associated with the aforementioned Dirac system.