On the profile of solutions for an elliptic problem arising in nonlinear optics

Daomin Cao; Ezzat S Noussair; Shusen Yan

doi:10.3934/dcds.2004.11.649

On the profile of solutions for an elliptic problem arising in nonlinear optics

Daomin Cao
, Ezzat S Noussair
, Shusen Yan

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We study the profile of solutions of [**EQUATION**] where λ > 0 is a parameter, h and g are nonnegative functions in L∞(ℝⁿ). We obtain the asymptotic behaviour of the least energy solutions or solutions obtained by the minimax principle. From the asymptotic behaviour we conclude that those solutions are asymmetric for λ large even if h and g are radially symmetric.

Original language	English
Pages (from-to)	649-666
Journal	Discrete and Continuous Dynamical Systems. Series A
Volume	11
Issue number	2-3
DOIs	https://doi.org/10.3934/dcds.2004.11.649
Publication status	Published - 2004

Keywords

Partial Differential Equations

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title = "On the profile of solutions for an elliptic problem arising in nonlinear optics",

abstract = "We study the profile of solutions of [**EQUATION**] where λ > 0 is a parameter, h and g are nonnegative functions in L∞(ℝⁿ). We obtain the asymptotic behaviour of the least energy solutions or solutions obtained by the minimax principle. From the asymptotic behaviour we conclude that those solutions are asymmetric for λ large even if h and g are radially symmetric.",

keywords = "Partial Differential Equations",

author = "Daomin Cao and Noussair, \{Ezzat S\} and Shusen Yan",

year = "2004",

doi = "10.3934/dcds.2004.11.649",

language = "English",

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T1 - On the profile of solutions for an elliptic problem arising in nonlinear optics

AU - Cao, Daomin

AU - Noussair, Ezzat S

AU - Yan, Shusen

PY - 2004

Y1 - 2004

N2 - We study the profile of solutions of [**EQUATION**] where λ > 0 is a parameter, h and g are nonnegative functions in L∞(ℝⁿ). We obtain the asymptotic behaviour of the least energy solutions or solutions obtained by the minimax principle. From the asymptotic behaviour we conclude that those solutions are asymmetric for λ large even if h and g are radially symmetric.

AB - We study the profile of solutions of [**EQUATION**] where λ > 0 is a parameter, h and g are nonnegative functions in L∞(ℝⁿ). We obtain the asymptotic behaviour of the least energy solutions or solutions obtained by the minimax principle. From the asymptotic behaviour we conclude that those solutions are asymmetric for λ large even if h and g are radially symmetric.

KW - Partial Differential Equations

U2 - 10.3934/dcds.2004.11.649

DO - 10.3934/dcds.2004.11.649

M3 - Article

SN - 1078-0947

VL - 11

SP - 649

EP - 666

JO - Discrete and Continuous Dynamical Systems. Series A

JF - Discrete and Continuous Dynamical Systems. Series A

IS - 2-3

ER -

On the profile of solutions for an elliptic problem arising in nonlinear optics

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