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)/2k≤(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 Sk,lSk,l with k−l≥3k−l≥3 to the result with any 0≤l≤k0≤l≤k.