The Nehari manifold for a fractional p-Laplacian system involving concave–convex nonlinearities

In this article, we are concerned with the multiplicity of solutions to the following fractional p-Laplacian system {(−Δ)psu=λ|u|q−2u+2αα+β|u|α−2u|v|β,inΩ;(−Δ)psv=μ|v|q−2v+2βα+β|u|α|v|β−2v,inΩ;u=v=0,inRn∖Ω, where ΩΩ is a smooth bounded set in RnRn, n>psn>ps with s∈(0,1)s∈(0,1) fixed, λ,μ>0λ,μ>0 are two parameters, 11,β>1α>1,β>1 satisfy p<α+β