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Open Journal of Mathematical Sciences (OMS)

ISSN: 2523-0212 (Online) 2616-4906 (Print)
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  • Research article

Picone type-identities for variable exponent p(⋅)-biharmonic operator and applications on stratified Lie groups

Abimbola Abolarinwa1
1Department of Mathematics, University of Lagos, Akoka, Lagos State, Nigeria
Copyright © Abimbola Abolarinwa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
  • Received: 14/01/2026
  • Revised: 10/02/2026
  • Accepted: 21/02/2026
  • Published: 09/03/2026

Abstract

In this paper we establish a new nonlinear variable exponent Picone-type identities for p(x)-biharmonic operator on a general stratified Lie group. As applications, eigenvalue properties, domain monotonicity, Barta-type estimate are proved for p(x)-sub-biharmonic operator. Furthermore, a Díaz-Saa-type inequality is proved and applied to study results on uniqueness of positive solutions of quasilinear elliptic equations involving variable exponent p(x)-sub-biharmonic operator.

Keywords: Biharmonic operator, Picone’s identity, variable Lebesgue spaces, eigenvalue problems, principal frequency, Hardy-Rellich inequalities