Changmu Chu, Tiaoyan Jiang, Jiaquan Liu, Multiple sign-changing solutions for a new nonlocal problem with critical growth

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DOI: 10.23952/jnva.10.2026.5.03

Volume 10, Issue 5, 1 October 2026, Pages 913-925

Abstract. In this paper, we study the following nonlocal problem

$\left (a- \lambda\int_{\Omega }\left | \nabla u \right | ^{2}dx \right )\Delta u +f(u)=0,$ in $\Omega,$
$u=0,$ on $\partial \Omega$ ,

where $\Omega \subset \mathbb{R}^N (N\geq 1)$ is a bounded smooth domain, $a$ and $\lambda$ are positive parameters, and $f$ is of subcritical or critical growth. By using the method of invariant sets for the descending flow, perturbation technique and necessary estimates, we establish the existence of infinitely many sign-changing solutions.

How to Cite this Article:
C. Chu, T. Jiang, J. Liu, Multiple sign-changing solutions for a new nonlocal problem with critical growth, J. Nonlinear Var. Anal. 10 (2026), 913-925.