Asymptotic formulas and critical exponents for two‐parameter nonlinear eigenvalue problems

Tetsutaro Shibata

Abstract and Applied Analysis, 2003, vol. 2003, issue 11, 671-684

Abstract: We study the nonlinear two‐parameter problem −u″(x) + λu(x) q = μu(x) p, u(x) > 0, x ∈ (0, 1), u(0) = u(1) = 0. Here, 1 0 are parameters. We establish precise asymptotic formulas with exact second term for variational eigencurve μ(λ) as λ → ∞. We emphasize that the critical case concerning the decaying rate of the second term is p = (3q − 1)/2 and this kind of criticality is new for two‐parameter problems.

Date: 2003
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https://doi.org/10.1155/S1085337503212045

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2003:y:2003:i:11:p:671-684

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