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

摘要

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