Infinitely many solutions for the Dirichlet problem involving the p-Laplacian in annulus

We present a result of existence of infinitely many solutions for the Dirichlet problem involving the p-Laplacian in annular domains, when $p\le N$, contouring the failure of compactness of $W^{1,p}(\mathrm{\Omega })$ in $C^0(\bar{\mathrm{\Omega }})$ applying a variable change.