Quadratic growth solutions of fully nonlinear elliptic equations with periodic data

Abstract In this paper, we study quadratic growth solutions of fully nonlinear elliptic equations of the form in , where is periodic and may be not uniformly elliptic. The existence of solutions and Liouville‐type results in the whole space and exterior domains are established, which generalize the classical results when is constant. As applications, the corresponding results are given to ‐Hessian equations, which include the celebrated results for Monge–Ampère equations.