Asymptotic behavior of blow up solutions to a class of prescribing Gauss curvature equations

The Liouville equation Δu+V(x)eu=0Δu+V(x)eu=0 has many applications in science and mathematics. One of the interesting features of solutions is their blow up behavior, a topic for which many results have been obtained. In this paper, we give a simple approach to obtaining a precise asymptotic expansion of a sequence of blow up solutions to the Liouville equation in a bounded domain Ω⊂R2Ω⊂R2.