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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Stability of variational eigenvalues for the fractional $p-$Laplacian

Pages: 1813 - 1845, Volume 36, Issue 4, April 2016      doi:10.3934/dcds.2016.36.1813

 
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Lorenzo Brasco - Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 39 Rue Frédéric Joliot Curie, 13453 Marseille, France (email)
Enea Parini - Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 39 Rue Frédéric Joliot Curie, 13453 Marseille, France (email)
Marco Squassina - Dipartimento di Informatica, Università di Verona, Strada Le Grazie 15, 37134 Verona, Italy (email)

Abstract: 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:  Fractional $p-$Laplacian, nonlocal eigenvalue problems, critical points, $\Gamma-$convergence.
Mathematics Subject Classification:  35P30, 49J35, 49J45.

Received: March 2015;      Revised: May 2015;      Available Online: September 2015.

 References