Linking solutions of critical p-Laplacian systems

In this paper we study the existence of nontrivial weak solutions for a suitable class of critical systems driven by the p-Laplacian operator under homogenous Dirichlet boundary conditions. The topological structure of the energy functional associated to the problem under consideration prevents the use of the classical Linking theorem, widely used in the current literature in several frameworks. For these reasons, we are led to adopt a different approach, relying on ℤ2-cohomological index theory and abstract Linking-type results. In our arguments a key tool is given by a topological property which naturally extends a classical result due to Degiovanni and Lancelotti to the case of systems. The methods developed here can be exploited to study other classes of nonlinear eigenvalue problems. Also, the existence theorems obtained in this paper improve some results already known in the literature. Moreover they extend well-known theorems for critical p-Laplacian equations to systems.