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Article Dans Une Revue Journal of Difference Equations and Applications Année : 2012

On Stepanov almost-periodic ocillations and their discretizations

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.
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Dates et versions

hal-00707827 , version 1 (13-06-2012)

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Jan Andres, Denis Pennequin. On Stepanov almost-periodic ocillations and their discretizations. Journal of Difference Equations and Applications, 2012, 18 (10), pp.1665-1682. ⟨10.1080/10236198.2011.587813⟩. ⟨hal-00707827⟩
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