Normalized Solutions for a Weighted Laplacian Problem with the Caffarelli-Kohn-Nirenberg Critical Exponent
Abstract
This article establishes the existence and multiplicity of normalized solutions to the weighted nonlinear Schrödinger-type equation governed by the Caffarelli-Kohn-Nirenberg operator, $$ -\text{div}(|x|^{-2a}\nabla u)=λ\frac{u}{|x|^{2a}}+β\frac{|u|^{q-2}u}{|x|^{bq}} +\frac{|u|^{2^{\sharp}-2}u}{|x|^{b{2^{\sharp}}}}\quad \text{in}~\mathbb{R}^N,$$ $$\int_{\mathbb{R}^N}\frac{|u|^2}{|x|^{2a}}dx=ρ^2,$$ where $λ\in \mathbb{R}$, $β,~ρ>0$, $0< a
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Advanced Mathematical Physics Problems
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 28 January 2026
- Document type
- Preprint