2025/03/20 by Xiaojun Chang, Vicenţiu D. Rădulescu, Chang, Xiaojun +3 · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2503.15858
openalex publication_date 2025/03/20 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28
In this paper, we investigate the following nonlinear Schrödinger equation with Neumann boundary conditions: \begincases -Δu+ λu= f(u) amp; \rm in ~ Ω,
(∂ u)/(∂ ν)=0 amp;\rm on ~∂ Ω\endcases coupled with a constraint condition: ∫Ω|u|2 dx=c, where Ω⊂ ℝN(N≥3) denotes a smooth bounded domain, ν represents the unit outer normal vector to ∂ Ω, c is a positive constant, and λ acts as a Lagrange multiplier. When the nonlinearity f exhibits a general mass supercritical growth at infinity, we establish the existence of normalized solutions, which are not necessarily positive solutions and can be characterized as mountain pass type critical points of the associated constraint functional. Our approach provides a uniform treatment of various nonlinearities, including cases such as f(u)=|u|p-2u, |u|q-2u+ |u|p-2u, and -|u|q-2u+|u|p-2u, where 2