Advances in Differential Equations

Single-peaks for a magnetic Schrödinger equation with critical growth

Sara Barile, Silvia Cingolani, and Simone Secchi

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Abstract

We prove existence results for complex-valued solutions for a semilinear Schrödinger equation with critical growth under the perturbation of an external electromagnetic field. Solutions are found via an abstract perturbation result in critical point theory, developed in [1, 2, 5].

Article information

Source
Adv. Differential Equations Volume 11, Number 10 (2006), 1135-1166.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867603

Mathematical Reviews number (MathSciNet)
MR2279741

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35B33: Critical exponents 47J30: Variational methods [See also 58Exx] 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)

Citation

Barile, Sara; Cingolani, Silvia; Secchi, Simone. Single-peaks for a magnetic Schrödinger equation with critical growth. Adv. Differential Equations 11 (2006), no. 10, 1135--1166. https://projecteuclid.org/euclid.ade/1355867603.


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