An abstract multiplicity result with applications to critical growth elliptic problems

We present some abstract multiplicity theorems that can be used to obtain multiple nontrivial solutions of critical growth p-Laplacian type problems. We show that the problems considered here have arbitrarily many solutions for all sufficiently large values of a certain parameter \lambda > 0. In particular, the number of solutions goes to infinity as \lambda \to \infty. Moreover, we give an explicit lower bound on \lambda in order to have a given number of solutions.