Topological degree for solutions of fourth order mean field equations

Changshou Lin; Juncheng Wei; Liping Wang

doi:10.1007/s00209-010-0690-9

Topological degree for solutions of fourth order mean field equations

Changshou Lin
, Juncheng Wei^*
, Liping Wang

^*此作品的通讯作者

数学科学学院

National Taiwan University
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 consider the following fourth order mean field equation with Navier boundary condition, where h is a C^2,β positive function, Ω is a bounded and smooth domain in ℝ⁴. We prove that for p ε (32mσ₃, 32(m+1)σ₃) the degree-counting formula for (*) is given by, where χ(Ω) is the Euler characteristic of Ω. Similar result is also proved for the corresponding Dirichlet problem,.

源语言	英语
页（从-至）	675-705
页数	31
期刊	Mathematische Zeitschrift
卷	268
期	3-4
DOI	https://doi.org/10.1007/s00209-010-0690-9
出版状态	已出版 - 8月 2011

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10.1007/s00209-010-0690-9

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title = "Topological degree for solutions of fourth order mean field equations",

abstract = "We consider the following fourth order mean field equation with Navier boundary condition, where h is a C2,β positive function, Ω is a bounded and smooth domain in ℝ4. We prove that for p ε (32mσ3, 32(m+1)σ3) the degree-counting formula for (*) is given by, where χ(Ω) is the Euler characteristic of Ω. Similar result is also proved for the corresponding Dirichlet problem,.",

author = "Changshou Lin and Juncheng Wei and Liping Wang",

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TY - JOUR

T1 - Topological degree for solutions of fourth order mean field equations

AU - Lin, Changshou

AU - Wei, Juncheng

AU - Wang, Liping

PY - 2011/8

Y1 - 2011/8

N2 - We consider the following fourth order mean field equation with Navier boundary condition, where h is a C2,β positive function, Ω is a bounded and smooth domain in ℝ4. We prove that for p ε (32mσ3, 32(m+1)σ3) the degree-counting formula for (*) is given by, where χ(Ω) is the Euler characteristic of Ω. Similar result is also proved for the corresponding Dirichlet problem,.

AB - We consider the following fourth order mean field equation with Navier boundary condition, where h is a C2,β positive function, Ω is a bounded and smooth domain in ℝ4. We prove that for p ε (32mσ3, 32(m+1)σ3) the degree-counting formula for (*) is given by, where χ(Ω) is the Euler characteristic of Ω. Similar result is also proved for the corresponding Dirichlet problem,.

UR - https://www.scopus.com/pages/publications/79960124889

U2 - 10.1007/s00209-010-0690-9

DO - 10.1007/s00209-010-0690-9

M3 - 文章

AN - SCOPUS:79960124889

SN - 0025-5874

VL - 268

SP - 675

EP - 705

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 3-4

ER -

Topological degree for solutions of fourth order mean field equations

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