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Asymptotic behavior of eigenvalues for two-parameter perturbed elliptic Sine-Gordon type equations

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Abstract

We consider two types of the perturbed elliptic Sine-Gordon type equations on an interval

$$\pm u^{\prime \prime}(t)+\lambda \ {\rm sin}\ u(t)=\mu f(u(t)),\ u(t)>0\ t\in I: =(-T,T),\ u(\pm T)=0,$$

where λ, μ > 0 are parameters and T > 0 is a constant. We shall establish asymptotic formulas for variational eigenvalues by using variational methods.

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Authors and Affiliations

  1. Institut de mathématique pure et appliquée, Université catholique de Louvain, Chemin du Cyclotron 2, B-1348, Louvain-la-Neuve, Belgium

    Tetsutaro Shibata

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  1. Tetsutaro Shibata
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Correspondence to Tetsutaro Shibata.

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Research supported by Japan Society for the Promotion of Science

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Shibata, T. Asymptotic behavior of eigenvalues for two-parameter perturbed elliptic Sine-Gordon type equations. Results. Math. 39, 155–168 (2001). https://doi.org/10.1007/BF03322681

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