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Localized nodal solutions for semiclassical nonlinear Schroedinger equations Wang, Zhi-Qiang
Description
We investigate the existence of localized sign-changing solutions for the semiclassical nonlinear Schr\"odinger equation $−\epsilon^2 \Delta v + V (x)v = |v|^{p-2} v, v \in H^1 (\mathbb{R}^N ) $ where $N \ge 2$, $2 < p < 2^*$, $\epsilon> 0$ is a small parameter, and V is assumed to be bounded and bounded away from zero. When V has a local minimum point P, as $\epsilon \to 0$, we construct an infinite sequence of localized sign-changing solutions clustered at P and these solutions are of higher topological type in the sense that they are obtained from a minimax characterization of higher dimensional symmetric linking structure via the symmetric mountain pass theorem. Our method combines the Byeon and Wang’s penalization approach and minimax method via a variant of the classical symmetric mountain pass theorem, and is rather robust without using any non-degeneracy conditions.
Item Metadata
Title |
Localized nodal solutions for semiclassical nonlinear Schroedinger equations
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2016-09-26T09:12
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Description |
We investigate the existence of localized sign-changing solutions for the semiclassical nonlinear Schr\"odinger equation $−\epsilon^2 \Delta v + V (x)v = |v|^{p-2} v, v \in H^1 (\mathbb{R}^N ) $ where $N \ge 2$, $2 < p < 2^*$, $\epsilon> 0$ is a small parameter, and V is assumed to be bounded and bounded away from zero. When V has a local minimum point P, as $\epsilon \to 0$, we construct an infinite sequence of localized sign-changing solutions clustered at P and these solutions are of higher topological type in the sense that they are obtained from a minimax characterization of higher dimensional symmetric linking structure via the symmetric mountain pass theorem. Our method combines the Byeon and Wang’s penalization approach and minimax method via a variant of the classical symmetric mountain pass theorem, and is rather robust without
using any non-degeneracy conditions.
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Extent |
41 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Utah State University
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Series | |
Date Available |
2017-06-15
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0348275
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International