Linking solutions for p-Laplace equations with nonlinearity at critical growth

Under a suitable condition on n and p, the quasilinear equation at critical growth − pu = λ|u|p−2u + |u|p∗−2u is shown to admit a nontrivial weak solution u ∈ W 1,p 0 (Ω) for any λ λ1. Nonstandard linking structures, for the associated functional, are recognized. © 2009 Elsevier Inc. All rights reserved.