Sign-changing solutions for the critical Neumann problem in the three-dimensional unit ball
Year: 2026
Type: preprint
Abstract: We consider the existence of nonradial sign-changing solutions to the problem $Δu-μu+|u|^4u=0$ with zero Neumann boundary conditions in the unit ball for an arbitrary fixed parameter $μ>0$. We prove that, for every $μ>0$, this problem admits infinitely many distinct nonradial sign-changing solutions. More precisely, for every sufficiently large even integer $K$, we construct a solution by gluing $K$ symmetrically arranged, suitably transformed copies of a sign-changing entire solution of the critical equation in $\mathbb{R}^3$. The construction combines an inner--outer gluing scheme with a finite-dimensional reduction. A detailed expansion of the reduced energy allows us to locate an interior critical point in the admissible parameter region and thereby complete the construction.
Source: arXiv (Cornell University)
Author: Wu, Fei
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220390117