Abstract
In this paper we are concerned with the existence and multiplicity of solutions of the following nonlocal system involving the fractional Laplacian
where \(\sigma \in (0,1)\), \(n \ge 1\), \((-\Delta )^\sigma \) denotes the fractional Laplacian of order \(\sigma \), \(a_i(x)\) are continuous and unbounded potentials which may change sign, and the nonlinearities \(f_i(x,u_1,\ldots ,u_m)\) are continuous functions which may be unbounded in x. We treat both the superquadratic situation and the nonquadratic situation at infinity on the nonlinearities \(f_i(x,u_1,\ldots ,u_m)\).
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Acknowledgements
The author would like to thank the referees for the careful review and the valuable comments, which provided insights that helped improve the paper. The author also would like to thank Princeton University, for its hospitality while part of this work was completed, and the Federal University of Paraíba for supporting his long term visit to Princeton University during the academic year 2017–2018.
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This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001 and CNPq Grant 306498/2016-2.
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de Souza, M. Existence and multiplicity of solutions for a class of fractional elliptic systems. Collect. Math. 71, 103–122 (2020). https://doi.org/10.1007/s13348-019-00253-6
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DOI: https://doi.org/10.1007/s13348-019-00253-6