A study on the number of sign-changing solutions of two-point boundary value problems and its application

两点边值问题变号解的个数及其应用研究

• 批准号: 20740082
• 负责人: TANAKA Satoshi
• 金额: $ 1.33万
• 依托单位: Okayama University of Science
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20740082/
• 关键词: 2点境界値問題; 符号変化する解; 球対称解; Emden-Fowler型方程式; 一意性; 正値解; Henon方程式; 符号の変化する解

In this study, two-point boundary value problems for nonlinear ordinary differential equations are considered. New results for the uniqueness of sign-changing solutions are established. As its application we have obtained sufficient conditions for the uniqueness of sign-changing radial solutions of boundary value problems of elliptic partial differential equations in a ball. Moreover the nonuniqueness examples for sign-changing radial solutions are also given. It is expected that we can obtain exact multiplicity results for sign-changing solutions of two-point boundary value problems by applying the method used here.

本文研究非线性常微分方程两点边值问题。建立了变号解的唯一性的新结果。作为应用，我们得到了球上椭圆型偏微分方程边值问题变号径向解唯一的充分条件。此外，还给出了变号径向解的非唯一性例子。应用本文的方法，我们可以得到两点边值问题变号解的精确多重性结果。

项目成果

On the nonuniqueness of positive solutions of boundary value problems for superlinear Emden-Fowler equations

超线性Emden-Fowler方程边值问题正解的非唯一性

• 发表时间: 2010
• 作者: Mervan Pasic;Satoshi Tanaka;田中敏
• 通讯作者: 田中敏

Uniqueness of nodal radial solutions superlinear elliptic equations in a ball

• DOI: 10.1017/s0308210507000431
• 发表时间: 2008-11
• 期刊: Proceedings of the Royal Society of Edinburgh: Section A Mathematics
• 作者: Satoshi Tanaka

On the uniqueness of positive solutions for two-point boundary value problems of Emden-Fowler differential equations

论Emden-Fowler微分方程两点边值问题正解的唯一性

• 发表时间: 2010
• 期刊: Mathematica Bohemica 135巻
• 作者: Taizou Sakamoto;Satoshi Tanaka;Satoshi Tanaka
• 通讯作者: Satoshi Tanaka

On the uniqueness of positive solutions of two-point BVPs of Emden-Fowler equations

论Emden-Fowler方程两点BVP正解的唯一性

• 发表时间: 2009
• 作者: Mervan Pasic;Satoshi Tanaka;田中敏;Satoshi Tanaka;Satoshi Tanaka;田中敏;Satoshi Tanaka;Satoshi Tanaka
• 通讯作者: Satoshi Tanaka

Uniqueness of positive solutions for two-point boundary value problems of Emden-Fowler differential equations

Emden-Fowler微分方程两点边值问题正解的唯一性

• 发表时间: 2009
• 作者: Mervan Pasic;Satoshi Tanaka;田中敏;Satoshi Tanaka;Satoshi Tanaka;田中敏;Satoshi Tanaka;Satoshi Tanaka;Satoshi Tanaka;Satoshi Tanaka;Satoshi Tanaka
• 通讯作者: Satoshi Tanaka