Asymptotic analysis and inverse problems of the nonlinear elliptic eigenvalue problems

非线性椭圆特征值问题的渐近分析与反问题

• 批准号: 21540219
• 负责人: SHIBATA Tetsutaro
• 金额: $ 2.75万
• 依托单位: Hiroshima University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540219/
• 关键词: 関数方程式論; 固有値; 漸近解析; 変分法; 逆問題

In this study, we investigated the precise asymptotic properties of the eigenfunctions and eigenvalues of nonlinear elliptic equations, and studied the inverse eigenvalue problems associated with thedirect problems. We clarify the global and local structures of the bifurcation curves for the equations with several types of nonlinear terms. As for inverse problems, we mainly studied the inverse bifurcation problems for logistic type equations. By using the theory of ordinary differential equations and the asymptotic expansion formulas for bifurcation curves, we determined the unknown nonlinear terms by the asymptotic behaviors of the bifurcation curves.

本文研究了非线性椭圆型方程本征函数和本征值的精确渐近性质，并研究了与正问题相关的本征值反问题。我们阐明了具有几种非线性项的方程分支曲线的整体和局部结构。在反问题方面，我们主要研究了Logistic型方程的反分支问题。利用常微分方程理论和分支曲线的渐近展开公式，由分支曲线的渐近性质确定未知非线性项。

项目成果

Asymptotic approach to inverse bifurcation problems for nonlinear Sturm-Liouville problems

非线性 Sturm-Liouville 问题的逆分岔问题的渐近方法

• 发表时间: 2012
• 期刊: Advanced Nonlinear Studies 12
• 作者: 本田あおい;岡崎悦明;佐藤坦;R.Kajikiya;田原秀敏＆山澤浩司;Kiyoshi Mochizuki;Tetsutaro Shibata
• 通讯作者: Tetsutaro Shibata

Precise asymptotics of boundary layers for damped simple pendulum equations

阻尼单摆方程边界层的精确渐近

• 发表时间: 2010
• 期刊: Results in Mathematics
• 影响因子: 2.2
• 作者: Hideo;Nakazawa;南就将;Tetsutaro Shibata;望月 清;渡邊道之;小林孝行;立川篤;望月 清;Tetsutaro Shibata
• 通讯作者: Tetsutaro Shibata

Asymptotic behave or of bifurcation curve for sine-Gordon type differential equation

正弦-Gordon型微分方程的分岔曲线的渐近特性

• DOI: 10.1155/2012/753857
• 发表时间: 2012
• 期刊: Abstract and Applied Analysis
• 作者: Y.Enatsu;Y.Nakata;Y.Muroya;Yousuke Ohyama;Tetsutaro Shibata
• 通讯作者: Tetsutaro Shibata

Critical exponents of the asymptotic formulas for two-parameter variational eigencurves

二参数变分特征曲线渐近公式的临界指数

• 发表时间: 2012
• 期刊: Differential and Integral Equations 25
• 作者: J. E. C. Lope;M. Roque and H. Tahara;Hiroshi Yanagihara;渡邊 道之;南 就将;Tetsutaro Shibata
• 通讯作者: Tetsutaro Shibata

Precise asymptotic behavior of solutions to damped simple pendulum equations

阻尼单摆方程解的精确渐近行为

• 发表时间: 2009
• 期刊: Electronic Journal of Differential Equations
• 影响因子: 0.7
• 作者: 渡辺宏太郎;塩路直樹;Tetsutaro Shibata
• 通讯作者: Tetsutaro Shibata