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Remarks on the existence theories of ordinary differential equations : 상미분 방정식의 존재성 이론에 관한 언급
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- Authors
- Advisor
- 하승열
- Major
- 자연과학대학 수리과학부
- Issue Date
- 2016-08
- Publisher
- 서울대학교 대학원
- Keywords
- Ordinary differential equations ; existence ; uniqueness ; Lipschitz condition ; Carathéodory theorem ; Osgood criterion ; Picard-Lindelöf theorem ; Peano theorem ; generalized theorem
- Description
- 학위논문 (석사)-- 서울대학교 대학원 : 수리과학부, 2016. 8. 하승열.
- Abstract
- In this thesis, we review the state-of-art in the existence theories of ordinary differential equations. More precisely, we discuss the Cauchy-Lipschitz theory, Carathéodory theory, Picard-Lindelöf theory, Peano theory and Osgood conditions for the classical solution. For discontinuous forcing, we introduce Filippov theory and generalized theory by Luigi Ambrosio, Camillo De Lellis and Gianluca Crippa.
- Language
- English
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