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The nonlinear version of Pazy’s local existence theorem

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Abstract

LetX be a real Banach space,U ⊂X a given open set,A ⊂X×X am-dissipative set andF:C(0,a;U) →L ∞(0,a;X) a continuous mapping. Assume thatA generates a nonlinear semigroup of contractionsS(t): {ie221-2}) → {ie221-3}), strongly continuous at the origin, withS(t) compact for allt>0. Then, for eachu 0 ∈ {ie221-4}) ∩U there existsT ∈ ]0,a] such that the following initial value problem: (du(t))/(dt) ∈Au(t) +F(u)(t),u(0)=u 0, has at least one integral solution on [0,T]. Some extensions and applications are also included.

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Authors and Affiliations

  1. Seminarul Matematic “Al. Myller”, Universitatea “Al. I. Cuza” Iaşi - 6600, The Socialist Republic of Romania

    Ioan I. Vrabie

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  1. Ioan I. Vrabie
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Vrabie, I.I. The nonlinear version of Pazy’s local existence theorem. Israel J. Math. 32, 221–235 (1979). https://doi.org/10.1007/BF02764918

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  • DOI: https://doi.org/10.1007/BF02764918

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