2012 Fiscal Year Final Research Report
Bifurcation analysis for nonlinear elliptic boundary value problems with combined nonlinearity of absorption and blowing up effects arising in population dynamics
| Project/Area Number |
22540170
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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 |
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Principal Investigator |
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| Project Period (FY) |
2010 – 2012
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| Keywords | 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 |
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| Research Abstract |
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.
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