Asymptotic behavior for the radial eigenvalues of p-Laplacian in certain annular domains

In this paper we prove an asymptotic behavior for the radial eigenvalues to the Dirichlet p-Laplacian problem \(-\Delta _p\,u = \lambda \,|u|^{p-2}u\) $-{\mathrm{\Delta }}_{p}u=\lambda {|u|}^{p-2}u$ in \(\Omega\) $\mathrm{\Omega }$ , \(u=0\) $u=0$ on \(\partial \Omega\) $\partial \mathrm{\Omega }$ , where \(\Omega\) $\mathrm{\Omega }$ is an annular domain \(\Omega =\Omega _{R,\overline{R}}\) $\mathrm{\Omega }={\mathrm{\Omega }}_{R,\overline{R}}$ in \(\mathbb {R}^N\) ${\mathbb{R}}^N$ .