Anisotropic Picone Type Identities for General Vector Fields and Some Applications

This extended abstract presents a generalisation of nonlinear Picone-type identities for anisotropic subelliptic p-Laplacian in the context of general vector fields, as proved in the forthcoming paper (Abolarinwa, Nonlinear Anisotropic Picone Type Identities for General Vector Fields and Applications, Submitted). Furthermore, several applications, which range from Hardy-type inequalities to Liouville-type and Sturmian-type comparison principles to first eigenvalue monotonicity, are highlighted. There is also an extension of these identities to subelliptic p-bi-Laplacian, and their applications to nonlinear eigenvalues in Abolarinwa (Nonlinear Anisotropic Picone Type Identities for General Vector Fields and Applications, Submitted).