Asymptotically ω-Periodic Functions in the Stepanov Sense and Its Application for an Advanced Differential Equation with Piecewise Constant Argument in a Banach Space

William Dimbour (1) , Solym Manou-Abi (2)

1 UMR 228 Espace-Dev, Espace pour le développement
2 IMAG - Institut Montpelliérain Alexander Grothendieck

In this paper, we give sufficient conditions for the existence and uniqueness of asymptotically ω-periodic solutions for a nonlinear differential equation with piecewise constant argument in a Banach space via asymptotically ω-periodic functions in the Stepanov sense. This is done using the Banach fixed point Theorem.

Domaines: Equations aux dérivées partielles [math.AP]

William Dimbour, Solym Manou-Abi. Asymptotically ω-Periodic Functions in the Stepanov Sense and Its Application for an Advanced Differential Equation with Piecewise Constant Argument in a Banach Space. Mediterranean Journal of Mathematics, 2018, 15 (1), ⟨10.1007/s00009-018-1071-6⟩. ⟨hal-02067045⟩