2009 Fiscal Year Final Research Report
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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| Keywords | 関数方程式 |
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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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