Existence and asymptotic behavior of entire large solutions for Hessian equations

Abstract

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 $|x{|}^{-l}$ at infinity for $l\le k-1$.