Linking and Multiplicity Results for the p-Laplacian on Unbounded Cylinders1

We consider the p-Laplacian problem − pu = λa x u p−2u + f x u in u ∈ W 1 p 0 on unbounded cylinders = × RN−m ⊂ RN N − m ≥ 2, where pu = div ∇u p−2∇u , λ is a constant in a certain range, and a ∈ LN/p ∩ L∞ is nonnegative a ≡ 0.Using the principle of symmetric criticality, existence and multiplicity are proved under suitable conditions on a and f .