Quasilinear elliptic system with coupling on nonhomogeneous critical term

We study the existence of multiple solutions for a quasilinear elliptic system of gradient type with the possibility of coupling on the critical and subcritical terms which are not necessarily homogeneous. The solutions are obtained from a version of the Symmetric Mountain Pass Theorem. A version of the Concentration-Compactness Principle for this class of systems allows us to verify that the Palais–Smale condition is satisfied below a certain level.