Some results for semi-stable radial solutions of $k$-Hessian equations

Miguel Angel Navarro; Justino Sanchez

Some results for semi-stable radial solutions of $k$-Hessian equations

Analysis of PDEs 2022-02-22 v1

Authors: Miguel Angel Navarro , Justino Sanchez

Abstract

We devote this paper to study semi-stable nonconstant radial solutions of $S_k(D^2u) = w(|x|)g(u)$ on the Euclidean space $R^n$ . We establish pointwise estimates and necessary conditions for the existence of such solutions (not necessarily bounded) for this equation. For bounded solutions we estimate their asymptotic behavior at infinity. All the estimates are given in terms of the spatial dimension $n$ , the values of $k$ and the behavior at infinity of the growth rate function of $w$ .

Keywords

k-hessian equations semi-stable solutions radial solutions pointwise estimates asymptotic behavior existence conditions

Cite

@article{arxiv.2202.09458,
  title  = {Some results for semi-stable radial solutions of $k$-Hessian equations},
  author = {Miguel Angel Navarro and Justino Sanchez},
  journal= {arXiv preprint arXiv:2202.09458},
  year   = {2022}
}

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