Some results for semi-stable radial solutions of k-Hessian equations with weight on ℝn

We devote this paper to study semi-stable nonconstant radial solutions of $S_k(D^2u)=w(\left \vert x \right \vert )g(u)$ on the Euclidean space $\mathbb {R}^n$. We establish pointwise estimates and necessary conditions for the existence of such solutions (not necessarily bounded) for this equation....

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Veröffentlicht in:Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2023-10, Vol.153 (5), p.1751-1776
Hauptverfasser: Navarro, Miguel Angel, Sánchez, Justino
Format: Artikel
Sprache:eng
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Zusammenfassung:We devote this paper to study semi-stable nonconstant radial solutions of $S_k(D^2u)=w(\left \vert x \right \vert )g(u)$ on the Euclidean space $\mathbb {R}^n$. 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 behaviour at infinity. All the estimates are given in terms of the spatial dimension $n$, the values of $k$ and the behaviour at infinity of the growth rate function of $w$.
ISSN:0308-2105
1473-7124
DOI:10.1017/prm.2022.73