Open Access Research

Semi-periodic solutions of difference and differential equations

Jan Andres1* and Denis Pennequin2

Author affiliations

1 Department of Mathematical Analysis, Faculty of Science, Palacký University, 17. listopadu 12, Olomouc, 771 46, Czech Republic

2 Centre PMF, Laboratoire SAMM, Université Paris I Panthéon-Sorbonne, 90, Rue de Tolbiac, Paris Cedex 13, 75 634, France

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Citation and License

Boundary Value Problems 2012, 2012:141  doi:10.1186/1687-2770-2012-141

Published: 28 November 2012

Abstract

The spaces of semi-periodic sequences and functions are examined in the relationship to the closely related notions of almost-periodicity, quasi-periodicity and periodicity. Besides the main theorems, several illustrative examples of this type are supplied. As an application, the existence and uniqueness results are formulated for semi-periodic solutions of quasi-linear difference and differential equations.

MSC: 34C15, 34C27, 34K14, 39A10, 42A16, 42A75.

Keywords:
semi-periodic sequences; semi-periodic functions; semi-periodic solutions; difference equations; differential equations