Nehari manifold approach for fractional p(.)-Laplacian system involving concave-convex nonlinearities

In this article, using Nehari manifold method we study the multiplicity of solutions of the nonlocal elliptic system involving variable exponents and concave-convex nonlinearities, $${ (-Δ)p(·)ˢ u=λ a(x)| u|q(x)-2u+α(x)/α(x) +β(x)c(x)| u|α(x)-2u| v| β(x), x∈ Ω; (-Δ)p(·)ˢ v=μ b(x)| v|q(x)-2v+α(x)/α(x) +β(x)c(x)| v|α(x)-2v| u| β(x), x∈ Ω; u=v=0, x∈ Ω^c:= R^NΩ, }$$ where \(Ω⊂ R^N\), \(N≥2\) is a smooth bounded domain, \(λ,μ>0\) are parameters, and \(s∈(0,1)\). We show that there exists \(Λ>0\) such that for all \(λ+μ<Λ\), this system admits at least two non-trivial and non-negative solutions under some assumptions on \(q,α,β,a,b,c\). For more information see https://ejde.math.txstate.edu/Volumes/2020/98/abstr.html