Multi-bump positive solutions of a fractional nonlinear Schrödingerequation in $\mathbb{R}^N$

Weiming  Liu; Lu  Gan

doi:10.3934/cpaa.2016.15.413

Article Contents

2016, Volume 15, Issue 2: 413-428. Doi: 10.3934/cpaa.2016.15.413

This issue Previous Article Boundary value problems for a semilinear elliptic equation with singular nonlinearity Next Article Schrödinger-Kirchhoff-Poisson type systems

Multi-bump positive solutions of a fractional nonlinear Schrödinger equation in $\mathbb{R}^N$

Weiming Liu^1, and
Lu Gan^1,

1.
School of Mathematics and Statistics, Hubei Normal University, Huangshi, 435002

Received: February 28, 2015

Revised: November 30, 2015

Published: February 2016

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Abstract

In this paper, we study a fractional nonlinear Schrödinger equation. Applying the finite reduction method, we prove that the equation has multi-bump positive solutions under some suitable conditions which are given in section 1.

Keywords:

Fractional nonlinear Schrödinger equation,
reduction method,
multi-bump solutions.

Mathematics Subject Classification: Primary: 35J10, 35B99; Secondary: 35J60.

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