Inserted: 13 mar 2015
Last Updated: 24 aug 2015
Journal: Discrete Contin. Dyn. Syst.
By virtue of $\Gamma-$convergence arguments, we investigate the stability of variational eigenvalues associated with a given topological index for the fractional $p-$Laplacian operator, in the singular limit as the nonlocal operator converges to the $p-$Laplacian. We also obtain the convergence of the corresponding normalized eigenfunctions in a suitable fractional norm.
Keywords: Gamma-convergence, critical points, nonlocal eigenvalue problems, Fractional p-Laplacian