Calculus of Variations and Geometric Measure Theory

D. Pagliardini - D. Mugnai

Existence and multiplicity results for the fractional Laplacian in bounded domains

created by pagliardini on 13 Oct 2016
modified on 29 May 2017


Published Paper

Inserted: 13 oct 2016
Last Updated: 29 may 2017

Journal: Advances in Calculus of Variations
Pages: 20
Year: 2015
Doi: 10.1515/acv-2015-0032

ArXiv: 1610.03734 PDF


In this paper, first we study existence results for a linearly perturbed elliptic problem driven by the fractional Laplacian. Then, we show a multiplicity result when the perturbation parameter is close to the eigenvalues. This latter result is obtained by exploiting the topological structure of the sublevels of the associated functional, which permits to apply a critical point theorem of mixed nature due to Marino and Saccon.