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Variational method for precise asymptotic formulas for nonlinear eigenvalue problems

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Abstract

We consider the nonlinear eigenvalue problem motivated by the perturbed elliptic sine-Gordon equation where p >1 is a constant and λ ∈ R is an eigenvalue parameter. Our aim is to clarify the asymptotic relationship between L p+1-norm, L ∞-norm of the solutions and λ when these norms are large. To this end, we consider an associated variational problem with this equation on a manifold new parameter), and obtain a solution pair . We establish the precise asymptotic formulas for .

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  1. Applied Mathematics Research Group, Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima, 739-8527, Japan

    Tetsutaro Shibata

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  1. Tetsutaro Shibata
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Correspondence to Tetsutaro Shibata.

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Shibata, T. Variational method for precise asymptotic formulas for nonlinear eigenvalue problems. Results. Math. 46, 130–145 (2004). https://doi.org/10.1007/BF03322876

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  • DOI: https://doi.org/10.1007/BF03322876

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