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Article Dans Une Revue Acta Scientiarum Mathematicarum Année : 2003

Blow-up" of bounded solutions of differential equations

Patrick Martinez
Michel Pierre
  • Fonction : Auteur
Judith Vancostenoble
  • Fonction : Auteur

Résumé

By the classical Cauchy-Lipschitz theory of ordinary differential equations, no maximal solution of $x' = f(t, x)$ can belong to some compact subset of the domain of definition $D$ of $f$. In the finite-dimensional case it follows that the maximal solutions are defined up to the boundary of $D$. Dieudonne and later Deimling gave counterexamples in some infinite-dimensional spaces: the maximal solution can remain bounded while it blows up in finite time. We give a complete, elementary and natural proof of this result for all infinite-dimensional Banach spaces.
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Dates et versions

hal-00084055 , version 1 (05-07-2006)

Identifiants

  • HAL Id : hal-00084055 , version 1

Citer

Vilmos Komornik, Patrick Martinez, Michel Pierre, Judith Vancostenoble. Blow-up" of bounded solutions of differential equations. Acta Scientiarum Mathematicarum, 2003, 69, num. 3-4, pp.651-657. ⟨hal-00084055⟩
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