Nontrivial solutions for a class of gradient-type quasilinear elliptic systems

The aim of this paper is investigating the existence of weak bounded solutions of a gradient-type system of m quasilinear elliptic equations, which generalizes the (p_1,...,p_m)- Laplacian system, on an open bounded domain. We prove that, under suitable hypotheses, the functional J related to such a problem is C^1 on a "good" Banach space X and satisfies the weak Cerami-Palais-Smale condition. Then, generalized versions of the Mountain Pass Theorems allow us to prove the existence of at least one critical point and, if J is even, of infinitely many ones, too.