Morse theory for a fourth order elliptic equation with exponential nonlinearity

Details Morse theory for a fourth order elliptic equation with exponential nonlinearity Morse theory for a fourth order elliptic equation with exponential nonlinearity

2009-11-13

arxiv.org/abs/0911.2563v1

Mathematics

Analysis of PDEs

13 pages, no figures

Scientific paper

In this paper we compute the Leray Schauder degree for a fourth order elliptic boundary value problem with exponential nonlinearity and Navier boundary condition. This will be made by proving a Poincare'-Hopf type theorem. Moreover by using this result, together with some quantitative results about the formal set of barycenters, we are able to establish a direct and geometrically clear degree counting formula for our problem. We remark that this formula has been proven with complete different methods by Lin Wei and Wang by using blow-up type estimates.

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