An Eigenvalue Problem for Nonlocal Equations


  • Giovanni Molica Bisci Mediterranean University of Reggio Calabria
  • Raffaella Servadei Università degli Studi di Urbino "Carlo Bo"



Fractional Laplacian, Nonlocal problems, Variational methods, Critical point theory


In this paper we study the existence of a positive weak solution for a class of nonlocal equations under Dirichlet boundary conditions and involving the regional fractional Laplacian operator...Our result extends to the fractional setting some theorems obtained recently for ordinary and classical elliptic equations, as well as some characterization properties proved for differential problems involving different elliptic operators. With respect to these cases studied in literature, the nonlocal one considered here presents some additional difficulties, so that a careful analysis of the fractional spaces involved is necessary, as well as some nonlocal L^q estimates, recently proved in the nonlocal framework.


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How to Cite

Molica Bisci, G., & Servadei, R. (2016). An Eigenvalue Problem for Nonlocal Equations. Bruno Pini Mathematical Analysis Seminar, 7(1), 69–84.