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

Abstract

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.