On the Existence of Viscosity Solutions of a Class of Nonlinear Second-order Elliptic Equations on Unbounded Domains

In this paper,the comparison principle for Dirichlet problem of a class of second-order nonlinear elliptic equations on unbounded domains is proved.Furthermore,the existence and uniqueness of viscosity solution of the problem are proved by constructing subsolution and supersolution together by applying Perron's method.