The exterior Dirichlet problem for Hessian quotient equations

In this paper, using a reverse MacLaurin inequality, we established the existence theorem of the exterior Dirichlet problem for Hessian quotient equations with a stronger asymptotic behavior at infinity. When k ≤ ( n + 1 ) / 2 , we improve the result in [L.M. Dai, The Dirichlet problem for Hessian quotient equations in exterior domains, J. Math. Anal. Appl. 380 (2011) 87–93] for S k , l with k − l ≥ 3 to the result with any 0 ≤ l ≤ k .