Almost periodic functions, Bohr compactification, and differential equations

1996 ◽  
Vol 66 (1) ◽  
pp. 149-158 ◽  
Author(s):  
Alexander Pankov
Keyword(s):  
Differential Equations ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Bohr Compactification

scholarly journals Notes on almost-periodicity in topological vector spaces

1986 ◽  
Vol 9 (1) ◽  
pp. 201-204 ◽  
Author(s):  
Gaston Mandata N'guérékata
Keyword(s):  
Differential Equations ◽  
Almost Periodic Functions ◽  
Vector Spaces ◽  
Almost Periodicity ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Topological Vector Spaces ◽  
Abstract Differential Equations

A study is made of almost-periodic functions in topological vector spaces with applications to abstract differential equations.

scholarly journals On some classes of almost periodic functions in abstract spaces

2004 ◽  
Vol 2004 (61) ◽  
pp. 3237-3247 ◽  
Author(s):  
Dariusz Bugajewski ◽  
Gaston M. N'Guérékata
Keyword(s):  
Banach Space ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Superposition Operator ◽  
Periodic Functions ◽  
Partial Differential ◽  
Abstract Spaces

We deal withC(n)-almost periodic functions taking values in a Banach space. We give several properties of such functions, in particular, we investigate their behavior in view of differentiation as well as integration. The superposition operator acting in the space of such functions is also under consideration. Some applications to ordinary as well as partial differential equations are presented. Moreover, we introduce the class of the so-called asymptoticallyC(n)-almost periodic functions and give some of their properties.

scholarly journals Almost periodic and asymptotically almost periodic type functions in Lebesgue spaces with variable exponents Lp(x)

Filomat ◽  
2020 ◽  
Vol 34 (5) ◽  
pp. 1629-1644
Author(s):  
Toka Diagana ◽  
Marko Kostic
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Almost Periodic Functions ◽  
Important Class ◽  
Variable Exponents ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Lebesgue Spaces ◽  
Asymptotically Almost Periodic

In this paper we introduce and analyze an important class of (asymptotically) Stepanov almost periodic functions in the Lebesgue spaces with variable exponents, which generalizes in a natural fashion all the (asymptotically) almost periodic functions. We then make extensive use of these new functions to study some abstract Volterra integro-differential equations in Banach spaces including multi-valued ones.

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