Asymptotic shape of solutions to nonlinear eigenvalue problems

Date

2005-03-29

Authors

Shibata, Tetsutaro

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University-San Marcos, Department of Mathematics

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 L<sup>1</sup>-norm of the solutions as λ → ∞.

Description

Keywords

Asymptotic formula, L1-norm, Simple pendulum, Logistic equation

Citation

Shibata, T. (2005). Asymptotic shape of solutions to nonlinear eigenvalue problems. <i>Electronic Journal of Differential Equations, 2005</i>(37), pp. 1-16.

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Attribution 4.0 International

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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