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arXiv · 2310.09579

Existence and asymptotic behavior of entire large solutions for Hessian equations

Xiang Li·Jiguang Bao
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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 $l\leq k-1$.

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Xiang Li, Jiguang Bao. 2023-10-14. Existence and asymptotic behavior of entire large solutions for Hessian equations. https://arxiv.org/abs/2310.09579

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