On completely integrable implicit ordinary differential equations

DOI 機関リポジトリ (HANDLE) オープンアクセス

説明

For smooth explicit n-th order ordinary differential equations, there exists a unique solution with initial condition and hence exists an n-parameter family of solutions at least locally. On the other hand, for smooth implicit ordinary differential equations, existence and uniqueness for solutions with initial condition does not hold. In this paper, we give a necessary and sufficient condition for existence of an n-parameter family of geometric solutions in the smooth category. Moreover, we give a sufficient condition that implicit ordinary differential equations have a unique geometric solution with initial condition. As a consequence, we classify completely integrable first and second ordinary differential equations in detail.

収録刊行物

キーワード

詳細情報 詳細情報について

  • CRID
    1390290699772161664
  • NII論文ID
    120006459658
  • DOI
    10.14943/84111
  • HANDLE
    2115/69771
  • 本文言語コード
    en
  • 資料種別
    departmental bulletin paper
  • データソース種別
    • JaLC
    • IRDB
    • CiNii Articles
  • 抄録ライセンスフラグ
    使用可

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