Nondegeneracy of positive solutions of semilinear elliptic problems in the hyperbolic space

Abstract

In this article, we will study the nondegeneracy properties of positive finite energy solutions of the equation -Δ 𝔹 u - λu = |u| p-1 u in the hyperbolic space. We will show that the degeneracy occurs only in an N-dimensional subspace. We will prove that the positive solutions are nondegenerate in the case of geodesic balls.