Work

Normalized solutions of mass supercritical Schrödinger equations with potential

Year: 2021

Type: article

Abstract: This paper is concerned with the existence of normalized solutions of the nonlinear Schrödinger equation −Δu+V(x)u+λu=|u|p−2u in RN in the mass supercritical and Sobolev subcritical case 2+4N<p<2*. We prove the existence of a solution (u,λ)∈H1(RN)×R+ with prescribed L2-norm ‖u‖2=ρ under various conditions on the potential V:RN→R, positive and vanishing at infinity, including potentials with singularities. The proof is based on a new min-max argument.

Source: Communications in Partial Differential Equations

DOI: 10.1080/03605302.2021.1893747

Authors: Thomas Bartsch, Riccardo Molle, Matteo Rizzi, Gianmaria Verzini

Institutions: Justus-Liebig-Universität Gießen, University of Rome Tor Vergata, Politecnico di Milano

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Alexander von Humboldt-Stiftung, Istituto Nazionale di Alta Matematica "Francesco Severi", Ministero dell’Istruzione, dell’Università e della Ricerca

Awards: G2813183223, G689437076