Admissible solutions to augmented nonsymmetric $k-$Hessian type equations I. The $d-$concavity of the $k-$Hessian type functions

Bang Tran Van, Ngoan Ha Tien, Tho Nguyen Huu +1

We establish for $2\le k\le n-1$ the strict concavity of the function $f_k(\lambda )=\log ({\sigma }_k(\lambda ))$ on a subset of the positive cone $Γ_n=\{λ=(λ_{1}, λ_{2}, \cdots,λ_{n})\in \mathbb{R}^n…