  We study the static black holes in the large $D$ dimensions in the
Gauss-Bonnet gravity with a cosmological constant, coupled to the Maxewell
theory. After integrating the equation of motion with respect to the radial
direction, we obtain the effective equations at large $D$ to describe the
nonlinear dynamical deformations of the black holes. From the perturbation
analysis on the effective equations, we get the analytic expressions of the
frequencies for the quasinormal modes of charge and scalar-type perturbations.
We show that for a positive Gauss-Bonnet term, the black hole could become
unstable only if the cosmological constant is positive, otherwise the black
hole is always stable. However, for a negative Gauss-Bonnet term, we find that
the black hole could always be unstable. The instability of the black hole
depends not only on the cosmological constant and the charge, but also
significantly on the Gauss-Bonnet term. Moreover, at the onset of instability
there is a non-trivial static zero-mode perturbation, which suggests the
existence of a new non-spherically symmetric solution branch. We construct the
non-spherical symmetric static solutions of the large $D$ effective equations
explicitly.
