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 $-\Delta_p u=\lambda |u|^{p-2}u+|u|^{p^*-2}\,u$ is shown to admit a nontrivial weak solution $u\in W^{1,p}_0(\Omega)$ for any $\lambda\geq\lambda_1$. Nonstandard linking structures, for the associated functional, are recognized.