Tyagi, JagmohanJagmohanTyagi2025-08-312025-08-312021-09-0110.1007/s40574-021-00276-72-s2.0-85099948210https://d8.irins.org/handle/IITG2025/25300We 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.falseBi-Laplacian | Hardy type inequality | p-Laplacian | Picone’s identity on hyperbolic space | Variational methodsArticle21982759429-439September 20211arJournal1