## Asymptotics for the principal eigenvalue of the $$p$$-biharmonic operator on the ball as $$p$$ approaches 1.(English)Zbl 1281.35061

Summary: Using the estimates of the principal eigenvalue of the $$p$$-biharmonic operator on the ball from below and from above, we provide its asymptotic analysis as $$p\to 1_+$$.

### MSC:

 35P15 Estimates of eigenvalues in context of PDEs 35J66 Nonlinear boundary value problems for nonlinear elliptic equations 35J60 Nonlinear elliptic equations 49R05 Variational methods for eigenvalues of operators
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### References:

 [1] Benedikt, J.; Drábek, P., Estimates of the principal eigenvalue of the $$p$$-biharmonic operator, Nonlinear Anal., 75, 5374-5379, (2012) · Zbl 1244.35096 [2] Benedikt, J., Continuous dependence of eigenvalues of $$p$$-biharmonic problems on $$p$$, Commun. Pure Appl. Anal., 12, 1469-1486, (2013) · Zbl 1267.34144 [3] Drábek, P.; Milota, J., (Methods of Nonlinear Analysis, Applications to Differential Equations, Birkhäuser Advanced Texts, (2007), Birkhäuser Basel, Boston, Berlin) · Zbl 1176.35002 [4] Drábek, P.; Ôtani, M., Global bifurcation result for the $$p$$-biharmonic operator, Electron. J. Differential Equations, 2001, 48, 1-19, (2001) · Zbl 0983.35099
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