## 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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