| Abstract: |
| We present an abstract multiplicity theorem 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. |
|