Asymptotic analysis for radial sign-changing solutions of the Brezis-Nirenberg problem in low dimensions

TL;DR

This paper investigates the asymptotic behavior of radial solutions with sign changes in the Brezis-Nirenberg problem within low-dimensional unit balls, revealing new insights into their limiting behavior as parameters vary.

Contribution

It provides a detailed asymptotic analysis of nodal radial solutions in low dimensions, a topic not thoroughly explored before in this context.

Findings

Characterization of the asymptotic behavior of solutions as parameters approach critical values

Identification of dimension-dependent phenomena in solution behavior

Insights into the structure of sign-changing solutions in low dimensions

Abstract

We consider the classical Brezis-Nirenberg problem in the unit ball of $\mathbb{R}^N$, $N\geq 3$ and analyze the asymptotic behavior of nodal radial solutions in the low dimensions $N=3,4,5,6$ as the parameter converges to some limit value which naturally arises from the study of the associated ordinary differential equation.