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

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.

Cited by in corpus (1)

• Nondegeneracy of critical points of the mean curvature of the boundary for Riemannian manifolds