  We construct a new analytic solution of Einstein-Born-Infeld-dilaton theory
in the presence of Liouville-type potentials for the dilaton field. These
solutions describe dilaton black holes with nontrivial topology and nonlinear
electrodynamics. Black hole horizons and cosmological horizons in these
spacetimes, can be a two-dimensional positive, zero or negative constant
curvature surface. The asymptotic behavior of these solutions are neither flat
nor (A)dS. We calculate the conserved and thermodynamic quantities of these
solutions and verify that these quantities satisfy the first law of black hole
thermodynamics.
