Strong Instability of Ground States to a Fourth Order Schrödinger Equation-Reference-Cited by-同舟云学术

Strong Instability of Ground States to a Fourth Order Schrödinger Equation

Published:2017-10-12 Issue:17 Volume:2019 Page:5299-5315
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Bonheure Denis¹²,Castéras Jean-Baptiste¹²,Gou Tianxiang³⁴,Jeanjean Louis³

Affiliation:

1. Département de Mathématiques, Université libre de Bruxelles, CP 214, Boulevard du triomphe, Bruxelles, Belgium

2. Équipe Mephysto, Inria Lille Nord-Europe, Parc Scientifique de la Haute-Borne Park Plaza Bâtiment A 40 avenue Halley, 59650 Villeneuve d’Ascq Cedex, France

3. Laboratoire de Mathématiques (UMR 6623), Université Bourgogne Franche-Comté, 16, Route de Gray, 25030 Besançcon Cedex, France

4. School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, People’s Republic of China

Abstract

Abstract In this note, we prove the instability by blow-up of the ground state solutions for a class of fourth order Schrödinger equations. This extends the first rigorous results on blowing-up solutions for the biharmonic nonlinear Schrödinger due to Boulenger and Lenzmann [8] and confirm numerical conjectures from [1–3, 11].

Funder

ERC

French National Research Agency

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2019/17/5299/29716961/rnx273.pdf

Reference17 articles.

1. “Singular solutions of the $L^2$-supercritical biharmonic nonlinear Schrödinger equation.”;Baruch,;Nonlinearity,2011

2. “Ring-type singular solutions of the biharmonic nonlinear Schrödinger equation.”;Baruch,;Nonlinearity,2010