## Topological Methods in Nonlinear Analysis

### Multiple positive solutions for fractional elliptic systems involving sign-changing weight

Haining Fan

#### Abstract

We study multiplicity results for positive solutions for a fractional elliptic system involving both concave-convex and critical growth terms. With the help of Nehari manifold and Ljusternik-Schnirelmann category, we investigate how the coefficient $h$ of the critical nonlinearity affects the number of positive solutions to this problem and get a relationship between the number of positive solutions and the topology of the global maximum set of $h$.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 49, Number 2 (2017), 757-781.

Dates
First available in Project Euclid: 28 May 2017

https://projecteuclid.org/euclid.tmna/1495936817

Digital Object Identifier
doi:10.12775/TMNA.2017.009

Mathematical Reviews number (MathSciNet)
MR3670485

Zentralblatt MATH identifier
1375.35179

#### Citation

Fan, Haining. Multiple positive solutions for fractional elliptic systems involving sign-changing weight. Topol. Methods Nonlinear Anal. 49 (2017), no. 2, 757--781. doi:10.12775/TMNA.2017.009. https://projecteuclid.org/euclid.tmna/1495936817