Singular limits in a liouville-type equation with singular sources

Chunyi Zhao

Singular limits in a liouville-type equation with singular sources

Chunyi Zhao^*

^*Corresponding author for this work

School of Mathematical Sciences

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

8 Scopus citations

Abstract

This paper considers the existence of multiple blowing up solutions for a Liouville-type equation -Δυ = ε²eυ - 4πΣ α_iδp_i with homogeneous Dirichlet conditions, where δ is the Dirac mass. We construct a solution which blows up at singular sources and other m points, and the solution satisfies ε² ∫ e^υ_ε → 8mπ + 8π σ(1 + α_i), provided α_i∉ ℕ.

Original language	English
Pages (from-to)	601-621
Number of pages	21
Journal	Houston Journal of Mathematics
Volume	34
Issue number	2
State	Published - 2008

Keywords

Blowing up solutions
Liouville equation
Singular sources

Cite this

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title = "Singular limits in a liouville-type equation with singular sources",

abstract = "This paper considers the existence of multiple blowing up solutions for a Liouville-type equation -Δυ = ε2eυ - 4πΣ αiδpi with homogeneous Dirichlet conditions, where δ is the Dirac mass. We construct a solution which blows up at singular sources and other m points, and the solution satisfies ε2 ∫ eυε → 8mπ + 8π σ(1 + αi), provided αi∉ ℕ.",

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author = "Chunyi Zhao",

year = "2008",

language = "英语",

volume = "34",

pages = "601--621",

journal = "Houston Journal of Mathematics",

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publisher = "University of Houston",

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T1 - Singular limits in a liouville-type equation with singular sources

AU - Zhao, Chunyi

PY - 2008

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N2 - This paper considers the existence of multiple blowing up solutions for a Liouville-type equation -Δυ = ε2eυ - 4πΣ αiδpi with homogeneous Dirichlet conditions, where δ is the Dirac mass. We construct a solution which blows up at singular sources and other m points, and the solution satisfies ε2 ∫ eυε → 8mπ + 8π σ(1 + αi), provided αi∉ ℕ.

AB - This paper considers the existence of multiple blowing up solutions for a Liouville-type equation -Δυ = ε2eυ - 4πΣ αiδpi with homogeneous Dirichlet conditions, where δ is the Dirac mass. We construct a solution which blows up at singular sources and other m points, and the solution satisfies ε2 ∫ eυε → 8mπ + 8π σ(1 + αi), provided αi∉ ℕ.

KW - Blowing up solutions

KW - Liouville equation

KW - Singular sources

UR - https://www.scopus.com/pages/publications/47649120588

M3 - 文章

AN - SCOPUS:47649120588

SN - 0362-1588

VL - 34

SP - 601

EP - 621

JO - Houston Journal of Mathematics

JF - Houston Journal of Mathematics

IS - 2

ER -

Singular limits in a liouville-type equation with singular sources

Abstract

Keywords

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