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

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
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References:

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