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

^*Corresponding author for this work

School of Mathematical Sciences

National Taiwan University
Chinese University of Hong Kong

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

6 Scopus citations

Abstract

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,.

Original language	English
Pages (from-to)	675-705
Number of pages	31
Journal	Mathematische Zeitschrift
Volume	268
Issue number	3-4
DOIs	https://doi.org/10.1007/s00209-010-0690-9
State	Published - Aug 2011

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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",

year = "2011",

month = aug,

doi = "10.1007/s00209-010-0690-9",

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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

Abstract

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