Let (M, g) be a smooth connected compact Riemannian manifold of finite dimension n ≥ 2 with a smooth boundary OM. We consider the problem {-ε2Δgu + u=|u|p-2u, u>0 on M, ∂u/∂v= 0 on ∂M, where v is an exterior normal to ∂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.
Ghimenti, M., Micheletti, A. (2010). Positive solutions of singularly perturbed nonlinear elliptic problem on riemannian manifolds with boundary. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 35(2), 319-337.
Positive solutions of singularly perturbed nonlinear elliptic problem on riemannian manifolds with boundary
GHIMENTI, MARCO GIPO;
2010
Abstract
Let (M, g) be a smooth connected compact Riemannian manifold of finite dimension n ≥ 2 with a smooth boundary OM. We consider the problem {-ε2Δgu + u=|u|p-2u, u>0 on M, ∂u/∂v= 0 on ∂M, where v is an exterior normal to ∂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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