Bifurcation analysis for nonlinear elliptic boundary value problems with combined nonlinearity of absorption and blowing up effects arising in population dynamics

群体动力学中吸收和爆炸效应组合非线性的非线性椭圆边值问题的分岔分析

• 批准号: 22540170
• 负责人: UMEZU Kenichiro
• 金额: $ 1.66万
• 依托单位: Ibaraki University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540170/
• 关键词: 関数方程式; 非線形楕円型境界値問題; 非線形境界条件; 人口動態論; 解析学; 非線形楕円型方程式; 爆発型非線形境界条件; 大域的分岐解析; 正値解; 折り返し点; 横断条件; ロジスティック; 漸近挙動; 一意性; 安定性; 分岐方程式

In this study, we consider the existence of positive solutions of nonlinear elliptic problems with nonlinear boundary conditions arising in population dynamics, by means of bifurcation analysis. The nonlinearity shows logistic nonlinearity combined with the power nonlinearity which means the incoming flux of population on the boundary. We determine the global behavior of bifurcation components of the positive solutions according to values of a parameter, and by this, we can also discuss the uniqueness and multiplicity of the positive solutions in some range of the parameter. The spatial heterogeneity of the indefinite coefficient equipped with the problem plays an important role.

在本研究中，我们通过分岔分析来考虑群体动力学中出现的具有非线性边界条件的非线性椭圆问题的正解的存在性。非线性表现为逻辑非线性与幂非线性相结合，即边界上的人口流入通量。我们根据参数的取值来确定正解分岔分量的全局行为，由此还可以讨论正解在参数的一定范围内的唯一性和多重性。问题所配备的不定系数的空间异质性起着重要作用。

项目成果

Global bifurcation results for semilinear elliptic boundary value problems with indefinite weights and nonlinear boundary conditions

具有不定权值和非线性边界条件的半线性椭圆边值问题的全局分岔结果

• DOI: 10.1007/s00030-010-0056-3
• 发表时间: 2010
• 作者: K.Umezu

Blowing-up properties of the positive principal eigenvalue for indefinite Robin-type boundary conditions

不定Robin型边界条件正主特征值的爆炸性质

• 发表时间: 2010
• 作者: Kenichiro Umezu

Global bifurcation of positive solutions for some elliptic problems with nonlinear boundary conditions

一些非线性边界条件椭圆问题正解的全局分岔

• 发表时间: 2010
• 作者: K.Umezu

Global bifurcation analysis of indefinite nonlinear boundary value problems with nonlinear boundary conditions

具有非线性边界条件的不定非线性边值问题的全局分岔分析

• 发表时间: 2010
• 作者: Kenichiro Umezu

Bifurcation approach to a logistic elliptic equation with a homogeneous incoming flux boundary condition

具有齐次流入通量边界条件的 Logistic 椭圆方程的分岔方法

• DOI: 10.1016/j.jde.2011.08.043
• 发表时间: 2012
• 作者: K.Umezu