Abstract: This paper introduces two novel nonlinear anisotropic Picone identities with variable exponents that expand upon the traditional identity used for the ordinary Laplace equation. Additionally, the research explores potential applications of these findings in anisotropic Sobolev spaces featuring variable exponents.
Keywords: anisotropic Picone identity; variable exponent
DOI: DOI 10.14712/1213-7243.2024.012
AMS Subject Classification: 35A23 35A02 35J75