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.

在本研究中，考虑非线性常微分方程的两点边值问题。建立了符号改变解决方案的独特性的新结果。作为其应用，我们获得了球内椭圆偏微分方程边值问题变号径向解唯一性的充分条件。此外还给出了变号径向解的非唯一性例子。期望通过应用这里使用的方法，我们可以获得两点边值问题的变号解的精确重数结果。

项目成果

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

Emden-Fowler方程两点边值问题正解的唯一性和非唯一性

• 发表时间: 2010
• 作者: Satoshi Tanaka

On the nonuniqueness of nodal radial solutions of sublinear elliptic equations in a ball

球内次线性椭圆方程节点径向解的非唯一性

• 发表时间: 2009
• 作者: 田中敏

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
• 作者: Satoshi Tanaka

Uniqueness of nodal radial solutions superlinear elliptic equations in a ball

球内超线性椭圆方程节点径向解的唯一性

• 发表时间: 2008
• 作者: Satoshi Tanaka

Emden-Fowler型微分方程式の2点境界値問題の正値解の一意性について

论Emden-Fowler型微分方程两点边值问题正确解的唯一性

• 发表时间: 2010
• 作者: 田中敏