| Existence and Uniqueness Theorem for the Cauchy Problem of Fuzzy Differential Equations under Non-Lipschitz Conditions |
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| 作者姓名： | 冯玉瑚 朱凡昌 |
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| 作者单位： | Department of Applied Mathematics，Donghua University，Shanghai，200051，professor，Department of Applied Mathematics，Donghua University，Shanghai，200051 |
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| 基金项目： | ThispaperispartiallysupportedbytheNationalNaturalScienceFoundationofChina,No :60 3 740 2 2 |
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| 摘 要： | IntroductionSince 196 5 ,whenZadeh publishedhis pioneeringpaper1] ,hundredsofexampleshavebeensuppliedwherethenatureofuncertaintyinthebehaviorofagivensystempossessesfuzzyratherthanstochasticnature Solutionsoffuzzydifferentialequationsprovideanoteworthyexampleoftime dependentfuzzysets Recently ,thetheoryoffuzzydifferentialequationshasbeeninitiatedandthebasicresultshavebeensystematicallyinvestigatedbymanyresearchers(e g see2 ,3,4 ,5 ]andtheirreferences) Therehavebeensometypicalresultsontheexi…
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Existence and Uniqueness Theorem for the Cauchy Problem of Fuzzy Differential Equations under Non-Lipschitz Conditions |
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| FENG Yu-hu,ZHU Fan-chang.Existence and Uniqueness Theorem for the Cauchy Problem of Fuzzy Differential Equations under Non-Lipschitz Conditions[J].Journal of Donghua University,2004,21(4). |
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| Authors: | FENG Yu-hu ZHU Fan-chang |
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| Institution: | Department of Applied Mathematics,Donghua University,Shanghai,200051 |
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| Abstract: | Solutions of fuzzy differential equations provide a noteworthy example of time-dependent fuzzy sets The purpose of this paper is to introduce functions of a suitable Lyapunov-like type and to show the existence and uniqueness theorem for the Cauchy problem of fuzzy differential equations under non-Lipschitz conditions The comparison principles and the existence and uniqueness theorems of this paper generalize many well-known results up to now |
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| Keywords: | Fuzzy set fuzzy differential equation existence and uniqueness non-Lipschitz condition |
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