The exterior Dirichlet problem for fully nonlinear elliptic equations related to the eigenvalues of the Hessian

In this paper, we establish the existence theorem for the exterior Dirichlet problems for a class of fully nonlinear elliptic equations, which are related to the eigenvalues of the Hessian matrix, with prescribed asymptotic behavior at infinity. This extends the previous results on Monge–Ampère equation and k-Hessian equation to more general cases, in particular, including the special Lagrangian equation.