  This paper aims to study the q-analogue of the Sturm Liouville problem and to
give an asymptotic behaviour at infinity for its solution '. Additionally, we
establish an asymptotic expansion of the q-Bessel function $j_\alpha$ for
$\alpha >-{1/2}. We are not in situation to claim that our results are new but
they have the advantage to show that the method used by Agranovich and
Marchenko remain true.
