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.
Degenerate p-Laplacian operators on H-type groups and applications to Hardy type inequalities
Unique Continuation for Schrödinger Evolutions, with applications to profiles of concentration and traveling waves
Five lectures on optimal transportation: Geometry, regularity and applications
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