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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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