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Estimates of the principal eigenvalue of the \(p\)-Laplacian. (English) Zbl 1245.35075

Summary: We provide estimates from below and from above for the principal eigenvalue of the \(p\)-Laplacian on a bounded domain. 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
35J92 Quasilinear elliptic equations with \(p\)-Laplacian
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[1] Drábek, P., Ranges of \(a\)-homogeneous operators and their perturbations, Časopis Pěst. mat., 105, 167-183, (1980) · Zbl 0427.47048
[2] Elbert, Á., A half-linear second order differential equation, (), 153-180
[3] Anane, A., Simplicité et isolation de la première valeur propre du \(p\)-laplacien avec poids, C. R. acad. sci. Paris Sér. I math., 305, 725-728, (1987) · Zbl 0633.35061
[4] Bhattacharya, T., Some results concerning the eigenvalue problem for the \(p\)-Laplacian, Ann. acad. sci. fenn. math., 14, 325-343, (1989) · Zbl 0701.35123
[5] Lindqvist, P., On the equation \(\operatorname{div}(| \nabla u |^{p - 2} \nabla u) + \lambda | u |^{p - 2} u = 0\), Proc. amer. math. soc., 109, 157-164, (1990) · Zbl 0714.35029
[6] Biezuner, R.J.; Ercole, G.; Martins, E.M., Computing the first eigenvalue of the \(p\)-Laplacian via the inverse power method, J. funct. anal., 257, 243-270, (2009) · Zbl 1172.35047
[7] Juutinen, P.; Lindqvist, P.; Manfredi, J.J., The \(\infty\)-eigenvalue problem, Arch. ration. mech. anal., 148, 89-105, (1999) · Zbl 0947.35104
[8] Kawohl, B., ()
[9] Allegretto, W.; Huang, Y.X., A picone’s identity for the \(p\)-Laplacian and applications, Nonlinear anal., 32, 819-830, (1998) · Zbl 0930.35053
[10] R.J. Biezuner, J. Brown, G. Ercole, E.M. Martins, Computing the first eigenpair of the \(p\)-Laplacian via inverse iteration of sublinear supersolutions. Preprint arXiv:1011.3172v2. · Zbl 1255.65205
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