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- Material Type
- 規格・テクニカルリポート類
- Author/Editor
- 梅津, 健一郎UMEZU, Kenichiro
- Author Heading
- Publication, Distribution, etc.
- Publication Date
- 2010-04-30
- Publication Date (W3CDTF)
- 2010
- Alternative Title
- Study on nonlinear elliptic boundary value problems with Allee effects, arising in population dynamicsアレー コウカ オ トモナウ ジンコウ ドウタイロン カラ ユライ スル ヒセンケイ ダエンガタ キョウカイチ モンダイ ノ ケンキュウ
- Target Audience
- 一般
- Note (General)
- 出版タイプ： VoRapplication/pdf研究報告書研究成果の概要（和文）：数理生物学に現れる人口動態モデルである非線形楕円型境界値問題の正値解の存在及び多重性を変分法と分岐理論を用いて示した．特に，分岐理論を援用して得た結果では，生物の条件的生存を導くアレー効果を示唆する分岐曲線の存在を示すことができた．また並行して，線形化固有値問題の主固有値を考察することによって，内包する係数に関する分岐点の依存性を調べ，分岐点が発散するための必要条件と十分条件を精密に与えた． 研究成果の概要（英文）：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.