Topological degree for solutions of fourth order mean field equations

Resource
Mathematische Zeitschrift, 268(3-4), 675-705
Journal
Mathematische Zeitschrift
Journal Volume
268
Journal Issue
3-4
Pages
675-705
Date Issued
2011
Author(s)
Wei, J.
Wang, L.
DOI
URI
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,. © 2010 Springer-Verlag.
Type
journal article
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