Differential and Integral Equations

Existence of a ground state and blow-up problem for a nonlinear Schrödinger equation with critical growth

Takafumi Akahori, Slim Ibrahim, Hiroaki Kikuchi, and Hayato Nawa

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

This paper is concerned with a focusing nonlinear Schrödinger equation whose nonlinearity consists of the energy-critical local interaction term with a perturbation of the $L^2$-super and energy-subcritical term. We prove the existence of a ground state (= a standing-wave solution of minimal action) when the space dimension is four or higher and prove the nonexistence of any ground state when the space dimension is three and the perturbation is small. Once we have a ground state, a so-called potential-well scenario works well, so that we can give a sufficient condition for the nonexistence of global-in-time solutions.

Article information

Source
Differential Integral Equations, Volume 25, Number 3/4 (2012), 383-402.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356012740

Mathematical Reviews number (MathSciNet)
MR2917888

Zentralblatt MATH identifier
1265.35329

Subjects
Primary: 35J20: Variational methods for second-order elliptic equations 35J61: Semilinear elliptic equations 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

Citation

Akahori, Takafumi; Ibrahim, Slim; Kikuchi, Hiroaki; Nawa, Hayato. Existence of a ground state and blow-up problem for a nonlinear Schrödinger equation with critical growth. Differential Integral Equations 25 (2012), no. 3/4, 383--402. https://projecteuclid.org/euclid.die/1356012740


Export citation