Concentrating solutions for an anisotropic elliptic problem with large exponent

Liping Wang; Dong Ye

doi:10.3934/dcds.2015.35.3771

Concentrating solutions for an anisotropic elliptic problem with large exponent

School of Mathematical Sciences

Université de Lorraine

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

2 Scopus citations

Abstract

We consider the following anisotropic boundary value problem [equation presented] where ω ∈ R² is a bounded smooth domain, p is a large exponent and a(x) is a positive smooth function. We investigate the effect of anisotropic coefficient a(x) on the existence of concentrating solutions. We show that at a given strict local maximum point of a(x), there exist arbitrarily many concentrating solutions.

Original language	English
Pages (from-to)	3771-3797
Number of pages	27
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	35
Issue number	8
DOIs	https://doi.org/10.3934/dcds.2015.35.3771
State	Published - 1 Aug 2015

Keywords

Anisotropic elliptic problem
Large exponent
Multi-bubble concentration

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10.3934/dcds.2015.35.3771

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title = "Concentrating solutions for an anisotropic elliptic problem with large exponent",

abstract = "We consider the following anisotropic boundary value problem [equation presented] where ω ∈ R2 is a bounded smooth domain, p is a large exponent and a(x) is a positive smooth function. We investigate the effect of anisotropic coefficient a(x) on the existence of concentrating solutions. We show that at a given strict local maximum point of a(x), there exist arbitrarily many concentrating solutions.",

keywords = "Anisotropic elliptic problem, Large exponent, Multi-bubble concentration",

author = "Liping Wang and Dong Ye",

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AU - Wang, Liping

AU - Ye, Dong

PY - 2015/8/1

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N2 - We consider the following anisotropic boundary value problem [equation presented] where ω ∈ R2 is a bounded smooth domain, p is a large exponent and a(x) is a positive smooth function. We investigate the effect of anisotropic coefficient a(x) on the existence of concentrating solutions. We show that at a given strict local maximum point of a(x), there exist arbitrarily many concentrating solutions.

AB - We consider the following anisotropic boundary value problem [equation presented] where ω ∈ R2 is a bounded smooth domain, p is a large exponent and a(x) is a positive smooth function. We investigate the effect of anisotropic coefficient a(x) on the existence of concentrating solutions. We show that at a given strict local maximum point of a(x), there exist arbitrarily many concentrating solutions.

KW - Anisotropic elliptic problem

KW - Large exponent

KW - Multi-bubble concentration

UR - https://www.scopus.com/pages/publications/84923769945

U2 - 10.3934/dcds.2015.35.3771

DO - 10.3934/dcds.2015.35.3771

M3 - 文章

AN - SCOPUS:84923769945

SN - 1078-0947

VL - 35

SP - 3771

EP - 3797

JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

IS - 8

ER -

Concentrating solutions for an anisotropic elliptic problem with large exponent

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Keywords

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