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

Tetsutaro Shibata

Abstract and Applied Analysis, 2003, vol. 2003, 1-14

Abstract:

We study the nonlinear two-parameter problem − u ″ ( x ) + λ u ( x ) q = μ u ( x ) p , u ( x ) > 0 , x ∈ ( 0 , 1 ) , u ( 0 ) = u ( 1 ) = 0 . Here, 1 < q < p are constants and λ , μ > 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 = ( 3 q − 1 ) / 2 and this kind of criticality is new for two-parameter problems.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:490369

DOI: 10.1155/S1085337503212045

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