On the positive vector solutions for nonlinear fractional Laplacian systems with linear coupling

Dengfeng Lü; Shuangjie Peng

doi:10.3934/dcds.2017141

Article Contents

2017, Volume 37, Issue 6: 3327-3352. Doi: 10.3934/dcds.2017141

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On the positive vector solutions for nonlinear fractional Laplacian systems with linear coupling

Dengfeng Lü^1,2, and
Shuangjie Peng^2,

1.
School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, China
2.
School of Mathematics and Statistics, Hubei Engineering University, Xiaogan 432000, China

Received: August 31, 2016

Revised: December 31, 2016

Published: May 2017

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Abstract

In this paper, a class of systems of two coupled nonlinear fractional Laplacian equations are investigated. Under very weak assumptions on the nonlinear terms $f$ and $g$, we establish some results about the existence of positive vector solutions and vector ground state solutions for the fractional Laplacian systems by using variational methods. In addition, we also study the asymptotic behavior of these solutions as the coupling parameter $β$ tends to zero.

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Mathematics Subject Classification: Primary: 35J50, 35A01; Secondary: 35B40.

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