Existence and asymptotic behavior of entire large solutions for Hessian equations

Xiang Li; Jiguang Bao

Existence and asymptotic behavior of entire large solutions for Hessian equations

Analysis of PDEs 2023-10-17 v1

Authors: Xiang Li , Jiguang Bao

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 $l\leq k-1$ .

Keywords

hessian equation entire large solutions existence nonexistence asymptotic behavior sublinear case

Cite

@article{arxiv.2310.09579,
  title  = {Existence and asymptotic behavior of entire large solutions for Hessian equations},
  author = {Xiang Li and Jiguang Bao},
  journal= {arXiv preprint arXiv:2310.09579},
  year   = {2023}
}

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