In this paper, we use the Limit Index Theory due to Li [A limit index theory and its applications, Nonlinear Anal. 25 (1995), 1371-1389] and the fractional version of concentration compactness ...principle to study the multiplicity of solutions for a class of noncooperative fractional ▫$p$▫-Laplacian elliptic system with homogeneous Dirichletboundary conditions involving the critical exponents.
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