  In this paper, we mainly establish the existence and uniqueness theorem for
solutions of the exterior Dirichlet problem for a class of fully nonlinear
second-order elliptic equations related to the eigenvalues of the Hessian, with
prescribed generalized symmetric asymptotic behavior at infinity. Moreover, we
give some new results for the Hessian equations, Hessian quotient equations and
the special Lagrangian equations, which have been studied previously.
