Fractional elliptic problems with critical growth in the whole of Rn [report]

Serena Dipierro, María Medina, Enrico Valdinoci, University, My, University, My
We study a nonlinear and nonlocal elliptic equation. The problem has a variational structure, and this allows us to find a positive solution by looking at critical points of a suitable energy functional. In particular, in this paper, we find a local minimum and a mountain pass solution of this functional. One of the crucial ingredient is a Concentration-Compactness principle. Some difficulties arise from the nonlocal structure of the problem and from the fact that we deal with an equation in
more » ... whole of the space (and this causes lack of compactness of some embeddings). We overcome these difficulties by looking at an equivalent extended problem.
doi:10.34657/2382 fatcat:snt4sqeqmvcwfagohkpndekzoq