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

TL;DR

This paper explores generic non-degeneracy properties of critical points of functionals and applies these findings to establish multiplicity results for solutions of a nonlinear PDE on compact Riemannian manifolds.

Contribution

It introduces new generic properties of non-degeneracy for critical points and applies them to prove multiple solutions for a nonlinear elliptic PDE on manifolds.

Findings

Established generic non-degeneracy properties of critical points.

Proved the existence of multiple solutions for the nonlinear PDE.

Applied theoretical results to specific geometric PDEs.

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 -{\epsilon}^2\Delta_g u+u=|u|p-2u in M, u in H_g^1(M) where M is a compact Riemannian manifold of dimension n and 2< p<2n/(n-2).