On doubly nonlocal fractional elliptic equations

  • Giovanni Molica Bisci

    Università degli Studi Mediterranea de Reggio Calabria, Italy
  • Dušan D. Repovš

    University of Ljubljana, Slovenia

Abstract

This work is devoted to the study of the existence of solutions to nonlocal equations involving the fractional Laplacian. These equations have a variational structure and we find a nontrivial solution for them using the Mountain Pass Theorem. To make the nonlinear methods work, some careful analysis of the fractional spaces involved is necessary. In addition, we require rather general assumptions on the local operator. As far as we know, this result is new and represent a fractional version of a classical theorem obtained working with Laplacian equations.

Cite this article

Giovanni Molica Bisci, Dušan D. Repovš, On doubly nonlocal fractional elliptic equations. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 26 (2015), no. 2, pp. 161–176

DOI 10.4171/RLM/700