Estimates of the principal eigenvalue of the \(p\)-biharmonic operator. (English) Zbl 1244.35096

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 \(p\)\(\to +\infty \).


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
Full Text: DOI


[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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.