• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Study on nonlinear elliptic boundary value problems with Allee effects, arising in population dynamics

Research Project

Project/Area Number 19540192
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionIbaraki University (2008-2009)
Maebashi Institute of Technology (2007)

Principal Investigator

UMEZU Kenichiro  Ibaraki University, 教育学部, 准教授 (00295453)

Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
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)
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
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.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (21 results)

All 2010 2009 2008 2007 Other

All Journal Article (8 results) (of which Peer Reviewed: 8 results) Presentation (10 results) Remarks (3 results)

  • [Journal Article] Global bifurcation results for semilinear elliptic boundary value problems with indefinite weights and nonlinear boundary conditions2010

    • Author(s)
      K. Umezu
    • Journal Title

      NoDEA (印刷中, 2010年出版予定)

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Blowing-up properties of the positive principal eigenvalue for indefinite Robin-type boundary conditions2010

    • Author(s)
      K. Umezu
    • Journal Title

      Rocky Mountain J.Math. (印刷中, 2010年出版予定)

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Global bifurcation results for semilinear elliptic boundary value problems with indefinite weights and nonlinear boundary conditions doi : 10.1007/s00030-010-0056-32009

    • Author(s)
      Kenichiro Umezu
    • Journal Title

      Nonlinear Differential Equations Appl.(NoDEA) (印刷中(オンラインで出版済))

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Positive solutions of semilinear elliptic eigenvalue problems with concave nonlinearities2007

    • Author(s)
      K. Umezu
    • Journal Title

      Advances in Differential Equations 12巻

      Pages: 1415-1436

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Blowing-up of principal eigenvalues for Neumann boundary conditions2007

    • Author(s)
      K. Umezu
    • Journal Title

      Proc.Roy.Soc.Edinburgh Section A 137巻

      Pages: 567-579

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Blowing-up of principal eigenvalues for Neumann boundary conditions2007

    • Author(s)
      Kenichiro Umezu
    • Journal Title

      Proceedings of the Royal Society of Edinburgh Section A: Mathematics 137

      Pages: 567-579

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Positive solutions of semilinear elliptic eigenvalue problems with concave nonlinearities2007

    • Author(s)
      Kenichiro Umezu
    • Journal Title

      Advances in Differential Equations 12

      Pages: 1415-1436

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Blowing-up properties of the positive principal eigenvalue for indefinite Robin-type boundary conditions

    • Author(s)
      Kenichiro Umezu
    • Journal Title

      Rocky Mountain Journal of Mathematics 印刷中

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] Global bifurcation for indefinite weighted elliptic problems with nonlinear boundary conditions2010

    • Author(s)
      梅津健一郎
    • Organizer
      日本数学会2010年年会函数方程式論分科会
    • Place of Presentation
      慶應義塾大学理工学部
    • Year and Date
      2010-03-25
    • Related Report
      2009 Annual Research Report 2009 Final Research Report
  • [Presentation] A super and subsolution method for sublinear problems with low regularity coefficients2008

    • Author(s)
      梅津健一郎
    • Organizer
      日本数学会2008年秋期総合分科会函数方程式論分科会
    • Place of Presentation
      東京工業大学理工学研究科
    • Year and Date
      2008-09-25
    • Related Report
      2009 Final Research Report
  • [Presentation] A super and subsolution method for sublinear problems with low regularity coefficients2008

    • Author(s)
      梅津健一郎
    • Organizer
      日本数学会2008総合分科会函数方程式論分科会
    • Place of Presentation
      東京工業大学理工学研究科
    • Year and Date
      2008-09-25
    • Related Report
      2008 Annual Research Report
  • [Presentation] Blowing-up properties of the positive principal eigenvalue for indefinite Robin-type boundary conditions2008

    • Author(s)
      K. Umezu
    • Organizer
      The 2^<nd> China-Japan Colloquium of Mathematical Biology
    • Place of Presentation
      岡山大学環境理工学部
    • Year and Date
      2008-08-06
    • Related Report
      2009 Final Research Report
  • [Presentation] Nehari manifold, fibering maps and semilinear elliptic boundary value problems2007

    • Author(s)
      梅津健一郎
    • Organizer
      数理科学セミナー
    • Place of Presentation
      同志社大学工学部
    • Year and Date
      2007-09-10
    • Related Report
      2009 Final Research Report
  • [Presentation] Nehari manifolds, fibering maps and semilinear elliptic boundary value problems2007

    • Author(s)
      梅津 健一郎
    • Organizer
      数理科学セミナー
    • Place of Presentation
      同志社大学工学部,京都府京田辺市
    • Year and Date
      2007-09-10
    • Related Report
      2007 Annual Research Report
  • [Presentation] Multiplicity of positive solutions to nonlinear elliptic boundary value problems arising in population dynamics2007

    • Author(s)
      K. Umezu
    • Organizer
      The workshop "Direct, Inverse and Control Problems for PDE's"
    • Place of Presentation
      Citta' Universitaria, Rome, Italy
    • Year and Date
      2007-06-27
    • Related Report
      2009 Final Research Report
  • [Presentation] Multiplicity of positive solutions to nonlinear elliptic boundary value problems arising in population dynamics2007

    • Author(s)
      梅津 健一郎
    • Organizer
      Direct, Inverse and Control Problems for PDE's
    • Place of Presentation
      ローマ大学,イタリア
    • Year and Date
      2007-06-27
    • Related Report
      2007 Annual Research Report
  • [Presentation] Principal eigenvalues of Neumann and Robin type eigenvalue problems with indefinite weights (招待講演)2007

    • Author(s)
      K. Umezu
    • Organizer
      The 4^<th> International Conference on Mathematical Biology
    • Place of Presentation
      Wuyishan, China
    • Year and Date
      2007-06-01
    • Related Report
      2009 Final Research Report
  • [Presentation] Principal eigenvalues of Neumann and Robin type eigenvalue problems with indefinite weights2007

    • Author(s)
      梅津 健一郎
    • Organizer
      The 4th International Conference on Mathematical Biology
    • Place of Presentation
      ウイシャン,中国
    • Year and Date
      2007-06-01
    • Related Report
      2007 Annual Research Report
  • [Remarks]

    • URL

      http://info.ibaraki.ac.jp/scripts/websearch/index.htm

    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://info.ibaraki.ac.jp/scripts/websearch/index.htm

    • Related Report
      2008 Annual Research Report
  • [Remarks]

    • URL

      http://umeken.sakura.ne.jp/kenwiki/index.php

    • Related Report
      2007 Annual Research Report

URL: 

Published: 2007-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi