Boundary Blow-up Solutions with a Spike Layer

Yihong Du; Shusen Yan

doi:10.1016/j.jde.2004.06.010

Boundary Blow-up Solutions with a Spike Layer

Yihong Du
, Shusen Yan

Mathematics

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

17 Citations (Scopus)

Abstract

We prove that for large λ>0, the boundary blow-up problem -Δu = -u(u - a)(1 - u) in Ω, u∣∂Ω=∞ has a solution with a spike located near the "most centered part" of Ω. Our proof is based on the reduction method and uses a "cut-off" technique to avoid the difficulties for the estimates near the boundary of Ω. Crown Copyright © 2004 Published by Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	156-184
Journal	Journal of Differential Equations
Volume	205
Issue number	1
DOIs	https://doi.org/10.1016/j.jde.2004.06.010
Publication status	Published - 2004

Keywords

Ordinary Differential Equations, Difference Equations and Dynamical Systems

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https://hdl.handle.net/1959.11/3644

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title = "Boundary Blow-up Solutions with a Spike Layer",

abstract = "We prove that for large λ>0, the boundary blow-up problem -Δu = -u(u - a)(1 - u) in Ω, u∣∂Ω=∞ has a solution with a spike located near the {"}most centered part{"} of Ω. Our proof is based on the reduction method and uses a {"}cut-off{"} technique to avoid the difficulties for the estimates near the boundary of Ω. Crown Copyright {\textcopyright} 2004 Published by Elsevier Inc. All rights reserved.",

keywords = "Ordinary Differential Equations, Difference Equations and Dynamical Systems",

author = "Yihong Du and Shusen Yan",

year = "2004",

doi = "10.1016/j.jde.2004.06.010",

language = "English",

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journal = "Journal of Differential Equations",

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T1 - Boundary Blow-up Solutions with a Spike Layer

AU - Du, Yihong

AU - Yan, Shusen

PY - 2004

Y1 - 2004

N2 - We prove that for large λ>0, the boundary blow-up problem -Δu = -u(u - a)(1 - u) in Ω, u∣∂Ω=∞ has a solution with a spike located near the "most centered part" of Ω. Our proof is based on the reduction method and uses a "cut-off" technique to avoid the difficulties for the estimates near the boundary of Ω. Crown Copyright © 2004 Published by Elsevier Inc. All rights reserved.

AB - We prove that for large λ>0, the boundary blow-up problem -Δu = -u(u - a)(1 - u) in Ω, u∣∂Ω=∞ has a solution with a spike located near the "most centered part" of Ω. Our proof is based on the reduction method and uses a "cut-off" technique to avoid the difficulties for the estimates near the boundary of Ω. Crown Copyright © 2004 Published by Elsevier Inc. All rights reserved.

KW - Ordinary Differential Equations, Difference Equations and Dynamical Systems

U2 - 10.1016/j.jde.2004.06.010

DO - 10.1016/j.jde.2004.06.010

M3 - Article

SN - 0022-0396

VL - 205

SP - 156

EP - 184

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 1

ER -

Boundary Blow-up Solutions with a Spike Layer

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