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Concentration phenomena arising in nonlinear partial differential equations

Research Project

Project/Area Number 23740079
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionOkayama University

Principal Investigator

OSHITA Yoshihito  岡山大学, 自然科学研究科, 准教授 (70421998)

Project Period (FY) 2011-04-28 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords楕円形方程式 / 非線形偏微分方程式 / 偏微分方程式 / 楕円型方程式 / 楕円型偏微分方程式
Outline of Final Research Achievements

We consider the equation nonlinear elliptic equations on Euclidean space, and study the case that the potential vanishes on a finite number of smooth compact framed sub manifolds in a critical frequency case. When the connected components of zero sets of the potential function are compact smooth framed manifolds, we consider the positive solutions which concentrates on the zero level manifolds, and that its limiting profiles are positive radially symmetric solutions in the space of the same dimension as the codimensions of the zero level manifolds.
Using Lyapunov--Schmidt reduction method, for a sequence of ε converging to zero, we will find a positive solution of the equation .

Report

(5 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (5 results)

All 2015 2014 2013 2011 Other

All Journal Article (1 results) (of which Peer Reviewed: 1 results) Presentation (4 results)

  • [Journal Article] STANDING WAVE CONCENTRATING ON COMPACT MANIFOLDS FOR NONLINEAR SCHRO ̈DINGER EQUATIONS2015

    • Author(s)
      J. Byeon, O. Kwon, Y. Oshita
    • Journal Title

      COMMUNICATIONS ON PURE AND APPLIED ANALYSIS

      Volume: 14 Issue: 3 Pages: 825-842

    • DOI

      10.3934/cpaa.2015.14.825

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Presentation] Concentration on compact manifolds for some nonlinear elliptic equations2014

    • Author(s)
      Yoshihito oshita
    • Organizer
      The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      Madrid
    • Year and Date
      2014-07-07 – 2014-07-11
    • Related Report
      2014 Annual Research Report
  • [Presentation] 複数の多様体上に集中したNLSの解2013

    • Author(s)
      大下承民
    • Organizer
      岡山理科大学における微分方程式セミナー
    • Place of Presentation
      岡山理科大学
    • Related Report
      2013 Research-status Report
  • [Presentation] コンパクト多様体上への集中2011

    • Author(s)
      大下承民
    • Organizer
      OCAMI 楕円型方程式研究集会~定常非線形シュレディンガー方程式の定在波解の研究~
    • Place of Presentation
      大阪市立大学
    • Related Report
      2011 Research-status Report
  • [Presentation] NLSに対するコンパクト多様体上への集中

    • Author(s)
      Yoshihito Oshita
    • Organizer
      広島大学数学教室談話会
    • Place of Presentation
      広島大学
    • Related Report
      2012 Research-status Report

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Published: 2011-08-05   Modified: 2019-07-29  

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