# Asymptotic shape of solutions to nonlinear eigenvalue problems

 dc.contributor.author Shibata, Tetsutaro dc.date.accessioned 2021-05-20T20:06:55Z dc.date.available 2021-05-20T20:06:55Z dc.date.issued 2005-03-29 dc.description.abstract We consider the nonlinear eigenvalue problem -u''(t) = ƒ(λ, u(t)), u > 0, u(0) = u(1) =0, where λ > 0 is a parameter. It is known that under some conditions on ƒ(λ, u), the shape of the solutions associated with λ is almost 'box' when λ ≫ 1. The purpose of this paper is to study precisely the asymptotic shape of the solutions as λ → ∞ from a standpoint of L1-framework. To do this, we establish the asymptotic formulas for L1-norm of the solutions as λ → ∞. dc.description.department Mathematics dc.format Text dc.format.extent 16 pages dc.format.medium 1 file (.pdf) dc.identifier.citation Shibata, T. (2005). Asymptotic shape of solutions to nonlinear eigenvalue problems. Electronic Journal of Differential Equations, 2005(37), pp. 1-16. dc.identifier.issn 1072-6691 dc.identifier.uri https://hdl.handle.net/10877/13611 dc.language.iso en dc.publisher Texas State University-San Marcos, Department of Mathematics dc.rights Attribution 4.0 International dc.rights.holder This work is licensed under a Creative Commons Attribution 4.0 International License. dc.rights.uri https://creativecommons.org/licenses/by/4.0/ dc.source Electronic Journal of Differential Equations, 2005, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. dc.subject Asymptotic formula dc.subject L1-norm dc.subject Simple pendulum dc.subject Logistic equation dc.title Asymptotic shape of solutions to nonlinear eigenvalue problems dc.type Article

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