  In this paper, considering the probe limit, we analytically study the onset
of holographic s-wave condensate in the planar Schwarzschild-AdS background.
Inspired by various low energy features of string theory, in the present work
we replace the conventional Maxwell action by a (non-linear) Born-Infeld (BI)
action which essentially corresponds to the higher derivative corrections of
the gauge fields. Based on a variational method, which is commonly known as the
Sturm-Liouville (SL) eigenvalue problem and considering a non-trivial
asymptotic solution for the scalar field, we compute the critical temperature
for the s-wave condensation. The results thus obtained analytically agree well
with the numerical findings\cite{hs19}. As a next step, we extend our
perturbative technique to compute the order parameter for the condensation.
Interestingly our analytic results are found to be of the same order as the
numerical values obtained earlier.
