Non degeneracy for solutions of singularly perturbed nonlinear elliptic problems on symmetric Riemannian manifolds

TL;DR

This paper investigates the genericity of nondegenerate sign-changing solutions to singularly perturbed nonlinear elliptic problems on symmetric Riemannian manifolds, establishing lower bounds on the number of such solutions.

Contribution

It provides new genericity results for nondegenerate solutions and quantifies the minimum number of sign-changing solutions on symmetric manifolds.

Findings

Genericity results for nondegenerate solutions

Lower bounds on the number of sign-changing solutions

Analysis with respect to parameters epsilon and metric g

Abstract

Given a symmetric Riemannian manifold (M, g), we show some results of genericity for non degenerate sign changing solutions of singularly perturbed nonlinear elliptic problems with respect to the parameters: the positive number {\epsilon} and the symmetric metric g. Using these results we obtain a lower bound on the number of non degenerate solutions which change sign exactly once.