Electron. J. Diff. Equ., Vol. 2015 (2015), No. 196, pp. 1-19.

Spike-layer solutions to nonlinear fractional Schrodinger equations with almost optimal nonlinearities

Jinmyoung Seok

In this article, we are interested in singularly perturbed nonlinear elliptic problems involving a fractional Laplacian. Under a class of nonlinearity which is believed to be almost optimal, we construct a positive solution which exhibits multiple spikes near any given local minimum components of an exterior potential of the problem.

Submitted February 3, 2015. Published July 30, 2015.
Math Subject Classifications: 35J10, 35J20, 35J60.
Key Words: Fractional Laplacian; spike solutions; nonlinear Schrodinger equations.

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Jinmyoung Seok
Department of Mathematics
Kyonggi University
154-42 Gwanggyosan-ro, Yeongtong-gu
Suwon 443-760, Korea
email: jmseok@kgu.ac.kr

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