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Article Dans Une Revue Proceedings of the American Mathematical Society Année : 2012

On the nonexistence of purely Stepanov almost-periodic solutions of ordinary differential equations

Résumé

It is shown that in uniformly convex Banach spaces, Stepanov almost-periodic functions with Stepanov almost-periodic derivatives are uniformly almost-periodic in the sense of Bohr. This in natural situations yields, jointly with the derived properties of the associated Nemytskii operators, the nonexistence of purely (i.e.nonuniformly continuous) Stepanov almost-periodic solutions of ordinary differential equations. In particular, the existence problem of such solutions, considered in a series of five papers of Z. Hu and A. B. Mingarelli, is answered in a negative way.

Dates et versions

hal-00707819 , version 1 (13-06-2012)

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Jan Andres, Denis Pennequin. On the nonexistence of purely Stepanov almost-periodic solutions of ordinary differential equations. Proceedings of the American Mathematical Society, 2012, 140, pp.2825-2834. ⟨10.1090/S0002-9939-2012-11154-2⟩. ⟨hal-00707819⟩
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