Linking and Multiplicity Results for the p-Laplacian on Unbounded Cylinders

We consider the p-Laplacian problem[formula]on unbounded cylinders Ω = Ω̃ × R^N − m  R^N, N − m ≥ 2, where Δ_pu = div(|u|^p − 2u), λ is a constant in a certain range, and a  L^N/p(Ω) ∩ L^∞(Ω) is nonnegative, a  0. Using the principle of symmetric criticality, existence and multiplicity are proved under suitable conditions on a and f.