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hal-00707827, version 1

On Stepanov almost-periodic ocillations and their discretizations

Jan Andres, Denis Pennequin (, http://samm.univ-paris1.fr/PENNEQUIN-Denis) 1

Journal of Difference Equations and Applications 18, 10 (2012) 1665-1682

Résumé : The relationship between Carathéodory almost-periodic (a.p.) solutions and their discretizations is clarified for differential equations and inclusions in Banach spaces. Our investigation was stimulated by an old result of Meisters [Proc. Am. Math. Soc. 10 (1959), pp. 113-119] about Bohr a.p. solutions which we generalize in several directions. Unlike for functions, Stepanov and Bohr a.p. sequences are shown to coincide. A particular attention is paid to purely (i.e. non-uniformly continuous) Stepanov a.p. solutions. Many ideas are explained in detail by means of examples illustrated.

  • 1 :  Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) (SAMM)
  • Université Paris I - Panthéon-Sorbonne
  • Domaine : Mathématiques/Analyse classique
    Mathématiques/Systèmes dynamiques
  • Mots-clés : Stepanov almost-periodic oscillations – almost-periodic sequences – non-uniformly continuous solutions – differential equations and inclusions in Banach spaces
 
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  • Contributeur : Denis Pennequin <>
  • Soumis le : Mercredi 13 Juin 2012, 15:36:34
  • Dernière modification le : Mardi 26 Février 2013, 22:05:13