Invariant Foliations for Carathéodory Type Differential Equations in Banach Spacesm

Throughout this paper we consider systems of differential equations of the form 1 https://www.w3.org/1998/Math/MathML"> x ˙ 1 = A 1 ( t ) x 1 + F 1 t , x 1 , x 2 , x ˙ 2 = A 2 ( t ) x 2 + F 2 t , x 1 , x 2 , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429217586/baa3656d-e71d-4ad9-8a66-0e62ece51d8b/content/eq3.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>