摘要：In this paper, we study the Monge–Ampère equations $\det D^{2}u=f$ in dimension two with f being a perturbation of $f_{0}$ at infinity. First, we obtain the necessary and sufficient conditions for the existence of radial solutions with prescribed asymptotic behavior at infinity to Monge–Ampère equations outside a unit ball. Then, using the Perron method, we get the existence of viscosity solutions with prescribed asymptotic behavior at infinity to Monge–Ampère equations outside a bounded domain.
关键词：Monge–Ampère equations ; Exterior Dirichlet problem ; Asymptotic behavior
