Asymptotic Approach to Inverse Bifurcation for Nonlinear Sturm-Liouville Problems

Author:

Shibata Tetsutaro1

Affiliation:

1. Graduate School of Engineering Hiroshima University, Higashi-Hiroshima, 739-8527, Japan

Abstract

Abstract We consider the nonlinear inverse bifurcation problem −u′′(t) + f (u(t)) = λu(t), u(t) > 0, t ∈ I := (0, 1), u(0) = u(1) = 0, where λ > 0 is a positive parameter, and the nonlinear term f (u) is unknown. We show that, if the asymptotic behavior of the Lq-bifurcation curve λ = λq(α) (1 ≤ q < ∞) of the positive solutions is understood well, then we are able to obtain f (u) and to characterize the asymptotic behavior of f(u) as u → ∞.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

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