New Solutions for nonlinear Schrödinger equations with critical nonlinearity

Title
New Solutions for nonlinear Schrödinger equations with critical nonlinearity
Publication Date
2007
Author(s)
Wei, Juncheng
Yan, Shusen
Type of document
Journal Article
Language
en
Entity Type
Publication
Publisher
Academic Press
Place of publication
United States of America
DOI
10.1016/j.jde.2007.03.001
UNE publication id
une:5762
Abstract
We consider the following nonlinear Schrödinger equations in ℝⁿ [**EQUATION**] where V (r) is a radially symmetric positive function. In [2] Ambrosetti, Malchiodi and Ni proved that if [**EQUATION**] has a nondegenerate critical point r₀ ≠ 0 then a layered solution concentrating near r₀ exists. In this paper, we show that if [**EQUATION**] and the dimension n= 3, 4 or 5, another new type of solution exists: this solution has a layer near r₀ and a bubble at the origin.
Link
link
Citation
Journal of Differential Equations, 237(2), p. 446-472
ISSN
1090-2732
0022-0396
Start page
446
End page
472

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