Some existence results for fully nonlinear elliptic equations of monge‐ampère type

Abstract

Abstract We study the existence and uniqueness of solutions of Monge‐Ampère‐type equations. This type of equations has been studied extensively by Caffarelli, Nirenberg, Spruck and many others. (See [5] through [8] and the references therein.) We present some existence and uniqueness results for this type of equations on compact Riemannian manifolds with non‐negative sectional curvature. We have also generalized some results in [7].