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The asymptotic behavior of Rayleigh quotients involving Luxemburg norms in Orlicz spaces L Ψ n is studied as n → ∞ , when (Ψ n) n is a sequence of N-functions. In a particular case, we recover a well-known result of Juutinen, Lindqvist & Manfredi and Fukagai, Ito & Narukawa regarding the limit, as p → ∞ , of the minima of Rayleigh quotients associated to the eigenvalue problem for the p-Laplacian. [ABSTRACT FROM AUTHOR]

We show that the spectrum of the relativistic mean curvature operator on a bounded domain Ω ⊂ ℝN (N ⩾ 1) having smooth boundary, subject to the homogeneous Dirichlet boundary condition, is exactly the interval (λ1(2), ∞), where λ1(2) stands for the principal frequency of the Laplace operator in Ω. [ABSTRACT FROM AUTHOR]

Abstract: The asymptotic behavior of Rayleigh quotients involving both Luxemburg norms and modulars in the variable exponent Lebesgue space is studied as . In a particular case, we recover a well-known result of Juutinen, Lindqvist and Manfredi regarding the limit, as of the minima of Rayleigh quotients associated to the eigenvalue problem for the p-Laplacian. [Copyright &y& Elsevier]

Abstract: Eigenvalue problems involving the p-Laplacian and rapidly growing operators in divergence form are studied in an Orlicz–Sobolev setting. An asymptotic analysis of these problems leads to a full characterization of the spectrum of an exponential type perturbation of the Laplace operator. [Copyright &y& Elsevier]