Variational Eigenvalues of the fractional $g$-Laplacian

TL;DR

This paper investigates the existence of variational eigenvalues for the fractional g-Laplacian operator under various boundary conditions, addressing challenges posed by its non-homogeneous, non-local nature.

Contribution

It introduces new methods to establish eigenvalue sequences for the fractional g-Laplacian with different boundary conditions, overcoming non-homogeneity issues.

Findings

Existence of eigenvalue sequences for the fractional g-Laplacian.

Results differ from classical power function cases due to non-homogeneity.

Addresses boundary conditions: Dirichlet, Neumann, Robin.

Abstract

In the present work we study existence of sequences of variational eigenvalues to non-local non-standard growth problems ruled by the fractional $g-$Laplacian operator with different boundary conditions (Dirichlet, Neumann and Robin). Due to the non-homogeneous nature of the operator several drawbacks must be overcome, leading to some results that contrast with the case of power functions.