Linking over cones and nontrivial solutions for p-Laplace equations with p-superlinear nonlinearity

We prove that the quasilinear equation -\Delta_p u=\lambda V |u|^{p-2}u+g(x,u), with g subcritical and p-superlinear at 0 and at infinity, admits a nontrivial weak solution u in W^{1,p}_0(\Omega) for any \lambda in R. A minimax approach, allowing also an estimate of the corresponding critical level, is used. New linking structures, associated to certain variational eigenvalues of -\Delta_p u=\lambda V |u|^{p-2}u, are recognized, even in absence of any direct sum decomposition of W^{1,p}_0(\Omega) related to the eigenvalue itself.