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 its applications to the Hessian equations, Hessian quotient equations and the special Lagrangian equations, which have been studied previously.

中文翻译：

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一类完全非线性椭圆方程的外部Dirichlet问题

在本文中，我们主要针对一类与Hessian特征值有关的完全非线性二阶椭圆型方程，在规定无穷大的广义对称渐近性质的情况下，建立外部Dirichlet问题解的存在性和唯一性定理。此外，我们将其应用于已经研究过的Hessian方程，Hessian商方程和特殊的Lagrangian方程。