Nonradial normalized solutions for nonlinear scalar field equations

By Louis Jeanjean, Sheng-Sen Lu. Nonlinearity, 2018

135 citations recorded by the source corpus.

We study the following nonlinear scalar field equation Here , m > 0 is a given constant and arises as a Lagrange multiplier. In a mass subcritical case but under general assumptions on the nonlinearity f , we show the existence of one nonradial solution for any , and obtain multiple (sometimes infinitely many) nonradial solutions when N = 4 or . In particular, all these solutions are sign-changing.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ccb3dce28b934fa9bc382b18ca550307b44f182b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Mathematical Physics

Citations in the corpus

A global branch approach to normalized solutions for the Schrödinger equation (2021, background): “Nowadays, this case is rather well-understood and we refer to [20, 22, 33, 36] for recent contributions.”
A mass supercritical problem revisited (2020, background): “In the present paper, regarding the issue of normalized nonradial sign-changing solutions, we somehow extend the existence and multiplicity results of [27] to the mass supercritical case.”
Normalized solutions for a Schrödinger equation with critical growth in RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{documen (2021, unknown): “For the reader interested in normalized solutions for the Schrödinger equations, we would also like to refer [9,11,12,17,25,29,31,34,38,39,41] and references therein.”