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

In this article, we will study the nondegeneracy properties of positive finite energy solutions of the equation -Delta(BN) u - lambda u = |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.