Study on nonlinear elliptic boundary value problems with Allee effects, arising in population dynamics
| Project/Area Number |
19540192
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Ibaraki University (2008-2009)
Maebashi Institute of Technology (2007) |
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Principal Investigator |
UMEZU Kenichiro Ibaraki University, 教育学部, 准教授 (00295453)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2007: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 関数方程式 / 非線形楕円型境界値問題 / 大域的分岐 / 正値解 / 符号不定な変係数 / 非線形境界条件 / 先験的評価 / 最大分岐成分 / 人口動態論 / 写像度の理論 / 符号変化する係数 / 線形化固有値問題 / 主固有値 / 凹型非線形楕円型方程式 / 変分法 / ネハリ多様体 |
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| Research Abstract |
We prove the existence and multiplicity of positive solutions of nonlinear elliptic boundary value problems arising in population dynamics, by using a variational technique and the bifurcation theory. Especially, we obtain some type of bifurcation of positive solutions, which suggests that the bifurcation component is derived from the Allee effect from population dynamics, implying a conditional persistence of species. We also discuss the dependence of the bifurcation point on coefficients included in the problem and give necessary and sufficient conditions for the blowing-up of the bifurcation point, by considering the positive principal eigenvalue of the associated, linearized eigenvalue problem.
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Report
(4 results)
Research Products
(21 results)
