Pseudo asymptotically periodic mild solutions of semilinear functional integro‐differential equations in Banach spaces

摘要

> In this paper, we introduce and investigate the functions of ( μ , ν )‐pseudo S ‐asymptotically ω ‐periodic of class r (class infinity). We systematically explore the properties of these functions in Banach space including composition theorems. As applications, we establish some sufficient criteria for ( μ , ν )‐pseudo S ‐asymptotic ω ‐periodicity of (nonautonomous) semilinear integro‐differential equations with finite or infinite delay. Finally, some interesting examples are presented to illustrate the main findings.