Positive solutions of singularly perturbed nonlinear elliptic problem on Riemannian manifolds with boundary

Details Positive solutions of singularly perturbed nonlinear elliptic problem on Riemannian manifolds with boundary Positive solutions of singularly perturbed nonlinear elliptic problem on Riemannian manifolds with boundary

2010-12-27

arxiv.org/abs/1012.5668v1

Topol. Methods Nonlinear Anal. 35 (2010), no. 2, 319-337

Mathematics

Analysis of PDEs

Scientific paper

Let (M,g) be a smooth connected compact Riemannian manifold of finite dimension n \geq 2 with a smooth boundary \partial M. We consider the problem -{\epsilon}^2\Delta_gu+u=|u|^{p-2}u, u>0 on M, \partial u/ \partial{\nu}=0 on \partial M where {\nu} is an exterior normal to \partial M. The number of solutions of this problem depends on the topological properties of the manifold. In particular we consider the Lusternik Schnirelmann category of the boundary.

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