## Abstract

In this paper, we study the existence and concentration of positive solution for the following class of fractional elliptic equation

where \(\epsilon \) is a positive parameter, *f* is a continuous function having a subcritical growth, *V* is a continuous potential possessing a local minimum, \(N > 2s,\)
\(s \in (0,1)\) and \( (-\Delta )^{s}u\) is the fractional laplacian.

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## Acknowledgments

This paper was completed while the second author named was visiting the Department of Mathematics of the Rutgers University, whose hospitality he gratefully acknowledges. He would like to express his gratitude to Professor Haim Brezis and Professor Yan Yan Li for invitation and friendship. The authors want to thank the anonymous Referee for his or her deep observations, careful reading and suggestions, which enabled us to improve this version of the manuscript.

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Communicated by P. Rabinowitz.

Research of C. O. Alves partially supported by CNPq/Brazil Proc. 304036/2013-7 and INCTMAT/CNPq/Brazi. O.H.M. was partially supported by INCTMAT/CNPq/Brazil, CNPq/Brazil Proc. 304014/2014-9 and CAPES/Brazil Proc. 2531/14-3.

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Alves, C.O., Miyagaki, O.H. Existence and concentration of solution for a class of fractional elliptic equation in \(\mathbb {R}^N\) via penalization method.
*Calc. Var.* **55**, 47 (2016). https://doi.org/10.1007/s00526-016-0983-x

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DOI: https://doi.org/10.1007/s00526-016-0983-x