Multiple solutions of an inhomogeneous Neumann problem for an elliptic system with critical Sobolev exponent

2012 ◽  
Vol 75 (4) ◽  
pp. 2047-2059
Author(s):  
Yajing Zhang
Keyword(s):  
Neumann Problem ◽  
Elliptic System ◽  
Multiple Solutions ◽  
Critical Sobolev Exponent ◽  
Sobolev Exponent

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

2016 ◽  
Vol 146 (6) ◽  
pp. 1167-1193 ◽  
Author(s):  
Wenjing Chen ◽  
Shengbing Deng
Keyword(s):  
Elliptic System ◽  
Multiple Solutions ◽  
Critical Sobolev Exponent ◽  
Nehari Manifold ◽  
Dirichlet Boundary Conditions ◽  
Bounded Set ◽  
Sobolev Exponent ◽  
Image Position ◽  
Two Parameters ◽  
The Nehari Manifold

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.

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