Picone identities for half-linear differential equations of fourth order

TL;DR

This paper develops Picone identities for half-linear fourth-order differential equations, extending known identities from linear cases and generalizing to multiple equations, providing new tools for analyzing complex differential systems.

Contribution

It introduces Picone identities for fourth-order half-linear ODEs and generalizes existing identities from second-order cases to multiple equations.

Findings

Established Picone identities for fourth-order half-linear ODEs.

Reduced to known identities in the linear case.

Generalized identities to sets of equations beyond two.

Abstract

Picone-type identities are established for half-linear ODEs of fourth order (one-dimensional p-biLaplacian). It is shown that in the linear case they reduce to the known identities for fourth order linear ODEs. Picone-type identity known for two half-linear second-order equations is also generalised to set of equations greater than two.