Multiplicity of positive solutions for a p–q-Laplacian system with concave and critical nonlinearities

In this paper, we consider a p–q  -Laplacian system with concave and Sobolev critical nonlinearities. By using the NNehari manifold, fibering maps and the Lusternik–Schnirelman category, we prove that the problem has at least cat(Ω)+1cat(Ω)+1 distinct positive solutions, where cat(Ω)cat(Ω) denotes the Lusternik–Schnirelman category of Ω in itself.