Hostname: page-component-7dd5485656-gs9qr Total loading time: 0 Render date: 2025-10-29T19:34:03.406Z Has data issue: false hasContentIssue false
  • English
  • Français

Multiple solutions for a critical fractional elliptic system involving concave–convex nonlinearities

Part of: Integral, integro-differential, and pseudodifferential operators Elliptic equations and systems

Published online by Cambridge University Press:  27 October 2016

Wenjing Chen  and
Shengbing Deng
Wenjing Chen
Affiliation:
School of Mathematics and Statistics, Southwest University, Chongqing 400715, People's Republic of China (wjchen@swu.edu.cn; shbdeng@swu.edu.cn)
Shengbing Deng
Affiliation:
School of Mathematics and Statistics, Southwest University, Chongqing 400715, People's Republic of China (wjchen@swu.edu.cn; shbdeng@swu.edu.cn)
Get access Rights & Permissions [Opens in a new window]

Extract

We are concerned with the multiplicity of solutions to the system driven by a fractional operator with homogeneous Dirichlet boundary conditions. Namely, using fibering maps and the Nehari manifold, we obtain multiple solutions to the following fractional elliptic system:

where Ω is a smooth bounded set in ℝn , n > 2s, with s ∈ (0, 1); (–Δ)s is the fractional Laplace operator;, λ, μ > 0 are two parameters; the exponent n/(n – 2s) ⩽ q < 2; α > 1, β > 1 satisfy is the fractional critical Sobolev exponent.

Keywords

critical fractional elliptic systemconcave–convex nonlinearitiesfibering mapsNehari manifold

MSC classification

Secondary: 35J20: Variational methods for second-order elliptic equations 35J60: Nonlinear elliptic equations 47G20: Integro-differential operators

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 146 , Issue 6 , December 2016 , pp. 1167 - 1193
Copyright
Copyright © Royal Society of Edinburgh 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable