Existence of multiple solutions for a fractional p-Laplacian system with concave-convex term

In this article, we study the existence of multiple solutions for the following system driven by a nonlocal integro-differential operator with zero Dirichlet boundary conditions

(0.1)$\{\begin{array}{c}{\left(-\Delta \right)}_p^{s}u=a\left(x\right){\left|u\right|}^{q-2}u+\frac{2\alpha }{\alpha +\beta }c\left(x\right){\left|u\right|}^{\alpha -2}u{\left|v\right|}^{\beta },\text{in}\Omega ,\\ {\left(-\Delta \right)}_p^{s}u=b\left(x\right){\left|v\right|}^{q-2}v+\frac{2\beta }{\alpha +\beta }c\left(x\right){\left|u\right|}^{\alpha }{\left|v\right|}^{\beta -2}v,\text{in}\Omega ,\\ u=v=0,in{R}^n\backslash \Omega ,\end{array}$

where O is a smooth bounded domain in Rⁿ, n > ps with s ? (0, 1) fixed, a(x), b(x), c(x) ≥ 0 and a(x), b(x), c(x) ? L^∞(0), 1 < q < p and α, β > 1 satisfy p < α + β < p*, p* =$\frac{np}{n-ps}$. By Nehari manifold and fibering maps with proper conditions, we obtain the multiplicity of solutions to problem (0.1).