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Elliptic Equation with Singular Terms on Riemannian Manifold

Authors:	Przemys?aw Górka

Institution:	(1) Department of Mathematics and Information Sciences, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland

Abstract:	In this paper we deal with the following equation: ${\Delta_g u -c u + \sum_{i=2}^l c_i u^i + \sum_{i=1}^{m} c_{-i} u^{-i} =0 }$ on a three-dimensional Riemannian manifold ${(\Sigma, g)}$ . We assume that the volume of Σ, the norm ${\|\|c_i\|\|_{H^2(\Sigma)}}$ , ${\|\|\nabla c\|\|_{L^2(\Sigma)}}$ and ${\|\|c-1\|\|_{L^{\infty}(\Sigma)}}$ are small enough. Using a rather simple argument we show the existence of solution to the problem. Dedicated to Gosia and Basia.

Keywords:	58J05 35J60 83C05
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