Differential and Integral Equations

Integral operators in spaces of bounded, almost periodic, and almost automorphic functions

Abstract

In this paper we consider integral operators on the real line and derive certain sufficient conditions under which the operators act as bounded linear operators between the spaces of Stepanov bounded functions. Next, we find conditions that insure the operators act between spaces of Stepanov almost periodic, or between spaces of Stepanov almost automorphic, functions. We apply these results to ordinary differential equations and obtain the existence and uniqueness of bounded, almost periodic, and almost automorphic solutions.

Article information

Source
Differential Integral Equations, Volume 21, Number 11-12 (2008), 1155-1176.

Dates
First available in Project Euclid: 14 December 2012