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Asymptotic behavior of eigenvalues of two-parameter nonlinear Sturm-Liouville problems

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Abstract

The nonlinear two-parameter Sturm-Liouville problemu "+μg(u)=λf(u) is studied for μ, λ>0. By using Ljusternik-Schnirelman theory on the general level set developed by Zeidler, we shall show the existence of ann-th variational eigenvalue λ=λn(μ). Furthermore, for specialf andg, the asymptotic formula of λ1(μ)) as μ→∞ is established.

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Authors and Affiliations

  1. Department of Mathematics, Aichi Prefectural University, 3-28 Takada-cho, Mizuho-ku, 467, Nagoya, Japan

    Tetsutaro Shibata

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  1. Tetsutaro Shibata
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Shibata, T. Asymptotic behavior of eigenvalues of two-parameter nonlinear Sturm-Liouville problems. J. Anal. Math. 66, 277–294 (1995). https://doi.org/10.1007/BF02788825

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  • DOI: https://doi.org/10.1007/BF02788825

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