The Nehari manifold for a fractional p-Laplacian system involving concave–convex nonlinearities. (February 2016) - Chen, Wenjing; Deng, Shengbing
Abstract: In this article, we are concerned with the multiplicity of solutions to the following fractional p-Laplacian system { ( − Δ ) p s u = λ | u | q − 2 u + 2 α α + β | u | α − 2 u | v | β, in Ω ; ( − Δ ) p s v = μ | v | q − 2 v + 2 β α + β | u | α | v | β − 2 v, in Ω ; u = v = 0, in R n ∖ Ω, where Ω is a smooth bounded set in R n, n > p s with s ∈ ( 0, 1 ) fixed, λ, μ > 0 are two parameters, 1 < q < p and α > 1, β > 1 satisfy p < α + β < p ∗, p ∗ = n p n − p s is the fractional Sobolev exponent, and ( − △ ) p s is the fractional p-Laplacian operator.