Multiplicity of positive solutions to a p–qp–q-Laplacian equation involving critical nonlinearity

In this paper, our main purpose is to establish the existence of multiple solutions of a p–qp–q-Laplacian equation with convex and Sobolev critical nonlinearity by some standard variational methods, whose key is to construct homotopies between ΩΩ and levels of the functional IθIθ, and some analytical techniques.