Picone's Identity for $p$-biharmonic operator and Its Applications

Gaurav Dwivedi

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arXiv · 1503.05535

Picone's Identity for $p$-biharmonic operator and Its Applications

Gaurav Dwivedi

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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.

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Gaurav Dwivedi. 2015-04-02. Picone's Identity for $p$-biharmonic operator and Its Applications. https://arxiv.org/abs/1503.05535

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