Asymptotic behavior for the radial eigenvalues of \(p\)-Laplacian in certain annular domains (Q6566494)

In this paper, the authors consider the following eigenvalue problem \N\[\N\begin{cases}\N-\Delta_p u=\lambda|u|^{p-2} u & \text { in } \Omega_{R, \bar{R}} \\\Nu=0 & \text { on } \partial \Omega_{R, \bar{R}}\N\end{cases} \N\]\Nwhere \(1<p \leq N\), \(\Omega_{R, \bar{R}}=\left\{x \in \mathbb{R}^N: R<|x|<\bar{R}\right\}\), with \(0<R<\bar{R}\) constants in \(\mathbb{R}\), is an annular domain.\N\NApplying the approach used in [\textit{M. Zhang}, J. Differ. Equations 166, 33--50 (2000; Zbl 0962.34062)], the authors prove an asymptotic behavior of the radial eigenvalues for the above problem.