PreprintarXiv licencearXiv
Normalized solutions to the NLS equation in the ball for any prescribed mass
Abstract
Given ρ>0, we consider the problem find $(λ,u) ∈ ℝ × H01(B)$ such that −Δu+λu = |u|p−1u & in B ∫B u2 dx = ρ, where B is a ball in ℝN, N ≥ 1, and 1<p<2*−1. Without any further restriction on N, ρ and p, we prove the existence of infinitely many radial solutions, and, in dimension N ≥ 4, of at least one non-radial solution.
Related
- Normalized solutions and small mass asymptotics for a nonlinear Dirac equation with a singular weight and competing powers
- Normalized solutions to critical and supercritical Schrödinger equations in a ball
- Normalized solutions to mass supercritical Schrödinger equations with radial potentials
- Interior curvature estimates for convex solutions of a prescribed curvature quotient equation
- Normalized solutions to an exponential growth Choquard equation driven by mixed local-nonlocal operator in ℝ2
BibTeX
@misc{soave2026normalized,
title = {{Normalized solutions to the NLS equation in the ball for any prescribed mass}},
author = {Nicola Soave},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15141},
eprint = {2609.15141},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15141},
}
RIS
TY - UNPB
TI - Normalized solutions to the NLS equation in the ball for any prescribed mass
AU - Nicola Soave
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15141
UR - https://arxiv.org/abs/2609.15141
AB - Given ρ>0, we consider the problem find $(λ,u) ∈ ℝ × H_0^1(B)$ such that −Δu+λu = |u|^p−1u & in B ∫_B u^2 dx = ρ, where B is a ball in ℝ^N, N ≥ 1, and 1<p<2^*−1. Without any further restriction on N, ρ and p, we prove the existence of infinitely many radial solutions, and, in dimension N ≥ 4, of at least one non-radial solution.
ER -