  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.
