The Dirichlet Problem for Nonsymmetric Augmented Hessian Quotient Type Equations

We deal with the Dirichlet problem for nonsymmetric augmented Hessian quotient type equations. First, we look for an admissible solution to the problem for corresponding symmetric augmented Hessian quotient type equations. Then we apply the Banach fixed point theorem to prove the existence of a $$\delta$$ -admissible solution in $$C^{2,\alpha }$$ to the problem by assuming that the augmented skew-symmetric matrix is sufficiently small in a certain sense. We also give a necessary condition for the existence and sufficient conditions for uniqueness of this kind of $$\delta$$ -admissible solutions.