Benedikt, Jiří; Drábek, Pavel Estimates of the principal eigenvalue of the \(p\)-biharmonic operator. (English) Zbl 1244.35096 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 13, 5374-5379 (2012). Summary: We provide estimates from below and from above for the principal eigenvalue of the \(p\)-biharmonic operator on a bounded domain with the Navier boundary conditions. We apply these estimates to study the asymptotic behavior of the principal eigenvalue for \(p\)\(\to +\infty \). Cited in 16 Documents MSC: 35P15 Estimates of eigenvalues in context of PDEs 35J66 Nonlinear boundary value problems for nonlinear elliptic equations 35J40 Boundary value problems for higher-order elliptic equations 49R05 Variational methods for eigenvalues of operators Keywords:eigenvalue problem for p-biharmonic operator; estimates of principal eigenvalue subject to Navier boundary conditions PDFBibTeX XMLCite \textit{J. Benedikt} and \textit{P. Drábek}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 13, 5374--5379 (2012; Zbl 1244.35096) Full Text: DOI References: [1] Drábek, P.; Ôtani, M., Global bifurcation result for the \(p\)-biharmonic operator, Electron. J. Differential Equations, 2001, 48, 1-19 (2001) · Zbl 0983.35099 [2] Benedikt, J.; Drábek, P., Estimates of the principal eigenvalue of the \(p\)-Laplacian, J. Math. Anal. Appl., 393, 311-315 (2012) · Zbl 1245.35075 [3] Allegretto, W.; Huang, Y. X., A Picone’s identity for the \(p\)-Laplacian and applications, Nonlinear Anal., 32, 819-830 (1998) · Zbl 0930.35053 [4] Jaroš, J., Picone’s identity for the \(p\)-biharmonic operator with applications, Electron. J. Differential Equations, 2011, 122, 1-6 (2011) · Zbl 1229.35024 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.