Ljusternik-Schnirelmann eigenvalues for the fractional m-Laplacian without the Δ2 condition

Abstract

This operator serves as a model for nonlocal, nonstandard growth diffusion problems. In contrast to previous analyses, we explore the eigenvalue problem without presuming the ∆2 condition on M – the primitive function of m. Our results show the existence of a sequence of eigenvalues λk → ∞. This research contributes to advancing our understanding of nonlocal diffusion models, specifically those characterized by the fractional m−Laplacian, by relaxing the constraints imposed by the ∆2 condition.