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arXiv · 1012.5668

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

Marco G. Ghimenti·Anna Maria Micheletti
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Abstract

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 -ε^2Δ_gu+u=|u|^{p-2}u, u>0 on M, \partial u/ \partialν=0 on \partial M where ν 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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Marco G. Ghimenti, Anna Maria Micheletti. 2010-12-27. Positive solutions of singularly perturbed nonlinear elliptic problem on Riemannian manifolds with boundary. https://arxiv.org/abs/1012.5668

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