Phantom with Born-Infeld-type Lagrangian

Recent analysis of the observation data indicates that the equation of state of the dark energy might be smaller than $-1,$ which leads to the introduction of phantom models featured by their negative kinetic energy to account for the regime of equation of state $w<\mathrm{}-1.$ In this paper, we generalize the idea to the Born-Infeld-type Lagrangian with a negative kinetic energy term and give the condition for the potential under which the late time attractor solution exists and also analyze a viable cosmological model in such a scheme.