Picone’s identity on hyperbolic space and its applications

We establish Picone’s identity for p-Laplace operator and biharmonic operator on hyperbolic space. We consider both, the ball model B^N and the half space model H^N. As an application of Picone’s identity, we show that the principal eigenvalue λ<inf>1</inf> of - Δ <inf>p</inf><inf>,</inf><inf>H</inf> is simple. We also obtain a Hardy type inequality on hyperbolic space.