Picone's identity for p-biharmonic operator and its applications

In this article we prove the nonlinear analogue of Picone's identity for p?biharmonic operator. As an application of our result we show that the Morse index of the zero solution to a p?biharmonic boundary value problem is 0. We also prove a Hardy type inequality and Sturmian comparison principle. We also show the strict monotonicity of the principle eigenvalue and linear relationship between the solutions of a system of singular p-biharmonic system.