Solutions with interior bubble and boundary layer for an elliptic problem

Liping Wang; Juncheng Wei

doi:10.3934/dcds.2008.21.333

Solutions with interior bubble and boundary layer for an elliptic problem

Liping Wang^*
, Juncheng Wei

^*此作品的通讯作者

Chinese University of Hong Kong

科研成果: 期刊稿件 › 文章 › 同行评审

6 引用（Scopus）

摘要

We study positive solutions of the equation ε² Δu -u + u ^n+2/n-2 = 0, where n = 3,4,5, and ε > 0 is small, with Neumann boundary condition in a smooth bounded domain Ω ⊂ R ⁿ. We prove that, along some sequence {ε_j} with ε_j -→ 0, there exists a solution with an interior bubble at an innermost part of the domain and a boundary layer on the boundary ∂Ω.

源语言	英语
页（从-至）	333-351
页数	19
期刊	Discrete and Continuous Dynamical Systems- Series A
卷	21
期	1
DOI	https://doi.org/10.3934/dcds.2008.21.333
出版状态	已出版 - 5月 2008
已对外发布	是

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abstract = "We study positive solutions of the equation ε2 Δu -u + u n+2/n-2 = 0, where n = 3,4,5, and ε > 0 is small, with Neumann boundary condition in a smooth bounded domain Ω ⊂ R n. We prove that, along some sequence \{εj\} with εj -→ 0, there exists a solution with an interior bubble at an innermost part of the domain and a boundary layer on the boundary ∂Ω.",

keywords = "Blow up, Critical sobolev exponent, Semilinear elliptic problem",

author = "Liping Wang and Juncheng Wei",

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AB - We study positive solutions of the equation ε2 Δu -u + u n+2/n-2 = 0, where n = 3,4,5, and ε > 0 is small, with Neumann boundary condition in a smooth bounded domain Ω ⊂ R n. We prove that, along some sequence {εj} with εj -→ 0, there exists a solution with an interior bubble at an innermost part of the domain and a boundary layer on the boundary ∂Ω.

KW - Blow up

KW - Critical sobolev exponent

KW - Semilinear elliptic problem

UR - https://www.scopus.com/pages/publications/44449086513

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DO - 10.3934/dcds.2008.21.333

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EP - 351

JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

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Solutions with interior bubble and boundary layer for an elliptic problem

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