Variational eigenvalues of the fractional g-Laplacian

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.

Keywords:

• Fractional Orlicz–Sobolev spaces
• Ljusternik–Schnirelman eigenvalues
• Minimax eigenvalues

AMS Subject Classifications:

• 46E30
• 35R11
• 45G05

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The third author was partially supported by Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET-Argentina).