Some generic properties of non degeneracy for critical points of functionals and applications

2011/06/02 by Marco Ghimenti, Ghimenti, Marco, Anna Maria Micheletti +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1106.0462

arxiv created 2011/06/02 · arxiv updated 2011/06/03

Abstract

We give some generic properties of non degeneracy for critical points of functionals. We apply these results, obtaining some theorems of multiplicity of solutions for the equation -ε²Δ_g u+u=|u|p-2u in M, u in H_g¹(M) where M is a compact Riemannian manifold of dimension n and 2< p<2n/(n-2).

Related

• Generic non-degeneracy of critical points of multiple Green functions on torus and applications to curvature equations
• Genericity of nondegenerate critical points and Morse geodesic functionals
• Critical points with prescribed energy for a class of functionals depending on a parameter: existence, multiplicity and bifurcation results
• Non-degeneracy of multi-bump solutions for the prescribed scalar curvature equations and applications
• Nondegeneracy of critical points of the mean curvature of the boundary for Riemannian manifolds