REMARK ON A SPECIAL CLASS OF FINSLER p-LAPLACIAN EQUATION

We investigate the anisotropic elliptic equation −∆^H_p u = g(u). Recently, Esposito, Riey, Sciunzi, and Vuono introduced an anisotropic Kelvin transform in their work [9] under the (H_M) condition, where H(ξ) = ^phMξ, ξi with a positive definite symmetric matrix M. Here, we emphasize that under the (H_M) assumption, the Finsler p-Laplacian and the classical p-Laplacian operator are equivalent following a linear transformation. This equivalence offers us a more direct way to derive and improve the main results in [9]. While this equivalence is elementary and noteworthy, to our knowledge, it seems have not been explicitly stated in the current literature.