Multiplicity results for critical p-biharmonic problems

We prove new multiplicity results for some critical growth p-biharmonic problems in bounded domains. More specifically, we show that each of the problems considered here has 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 -> infinity. We also give an explicit lower bound on lambda$\lambda$ in order to have a given number of solutions. This lower bound will be in terms of an unbounded sequence of eigenvalues of a related eigenvalue problem. Our multiplicity results are new even in the semilinear case p=2. The proofs are based on an abstract critical point theorem.