Asymptotic behavior of the eigenvalues of the p-Laplacian. (English) Zbl 0704.35108
The author gives an estimate, from above and below, for the counting function of the eigenvalue problem:
\[
div(| \nabla u|^{p- 2}\cdot \nabla u)+\lambda | u|^{p-2}u=0;\;u=0\text{ on } \partial \Omega
\]
\(\Omega\) is a bound domain of \({\mathbb{R}}^ n\).
Reviewer: D.Robert
MSC:
| 35P20 | Asymptotic distributions of eigenvalues in context of PDEs |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
| 35P30 | Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs |
References:
| [1] | Garcia Azorero J.P., Commun. in PDE 12 pp 1389– (1987) · doi:10.1080/03605308708820534 |
| [2] | Garcia Azorero, J.P. and Peral Alonso, I. 1988. ”Comportement asymptotique des valeurs propres du {\(\phi\)}–laplacien”. Vol. 301, Ser I, 75–78. Paris: C.R.Acad.Sci. |
| [3] | Rabinowitz Paul H., Rocky Mountain J. 3 pp 161– (1973) · Zbl 0255.47069 · doi:10.1216/RMJ-1973-3-2-161 |
| [4] | Amann H., Math. Ann. 199 pp 55– (1972) · Zbl 0233.47049 · doi:10.1007/BF01419576 |
| [5] | Taylor M.E., Pseudodifferential Operators (1981) · Zbl 0453.47026 |
| [6] | Spanier, Algebraic Topology (1966) |
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