Existence and asymptotic behavior of entire large solutions for Hessian equations

In this paper, we give some existence and nonexistence results for nonradial entire large solutions of the Hessian equation $S_k\left(D^{2}u\right)=b(x)u^{\gamma }$ in the sublinear case $0<\gamma <k$. The exact asymptotic behavior of large solutions at infinity is also studied when $b(x)$ is the oscillation of a radial function $\mathrm{\mid }x{\mathrm{\mid }}^{-l}$ at infinity for $l\le k-1$.