Abstract
In this paper we extend the well-known concentration-compactness principle for the Fractional Laplacian operator in unbounded domains. As an application we show sufficient conditions for the existence of solutions to some critical equations involving the fractional p-Laplacian in the whole \({\mathbb {R}}^n\).
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Acknowledgements
This paper was supported by Grants UBACyT 20020130100283BA, CONICET PIP 11220150100032CO and ANPCyT PICT 2012-0153. The authors are members of CONICET.
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Bonder, J.F., Saintier, N. & Silva, A. The concentration-compactness principle for fractional order Sobolev spaces in unbounded domains and applications to the generalized fractional Brezis–Nirenberg problem. Nonlinear Differ. Equ. Appl. 25, 52 (2018). https://doi.org/10.1007/s00030-018-0543-5
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DOI: https://doi.org/10.1007/s00030-018-0543-5