An inverse iteration method for obtaining q-eigenpairs of the p-Laplacian in a general bounded domain

Let $\Omega$ be a bounded and smooth domain of $\mathbb{R}^{N}$, $N\geq2$, and consider the eigenvalue problem: $-\Delta_{p}u=\lambda\left\Vert u\right\Vert _{L^{q}(\Omega)}^{p-q}\left\vert u\right\vert ^{q-2}u$ in $\Omega,$ $u=0$ on $\partial\Omega,$ where $p>1$, $1\leq q