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semi-stable solutions

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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Some results for semi-stable radial solutions of k-Hessian equations with weight on ℝn
Part of
- Elliptic equations and systems
- Partial differential equations
Miguel Angel Navarro, Justino Sánchez
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 153 / Issue 5 / October 2023

Published online by Cambridge University Press:

15 November 2022, pp. 1751-1776

Print publication:

October 2023
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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 $w$.