Work

Normalized solutions to mass supercritical Schrödinger equations with radial potentials

Year: 2026

Type: article

Abstract: We study the stationary nonlinear Schrödinger equation $$-\Delta u+V(x)u+\lambda u=|u|^{q-2}u, \quad u \in H^1(\mathbb{R}^N), \quad N \geq 2,$$ where $V \in L^{\infty}(\mathbb{R}^N)$ is a radial potential. In the $L^2$-supercritical regime, we show the existence of an explicit $\mu_0 >0$ such that, for any $\mu \in (0, \mu_0)$, the equation admits two solutions having $L^2$ norm $\mu$. The potential $V$ is not assumed to have a sign, nor a specific behavior at infinity and only a low regularity is required. Our proof relies on the use of Morse type information, on some spectral arguments, and on a blow-up analysis developed in a radial setting.

Source: Journal of Differential Equations

DOI: 10.1016/j.jde.2026.114671

Authors: Pablo Carrillo, Louis Jeanjean

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funder: Agence Nationale de la Recherche

Award: Nonlinear Quantum Graphs