  The purpose of the present paper is to study representations and cohomologies
of differential 3-Lie algebras with any weight. We introduce the representation
of a differential 3-Lie algebra. Moreover,we develop cohomology theory of a
differential 3-Lie algebra. We also depict the relationship between the
cohomologies of a differential 3-Lie algebra and its associated differential
Leibniz algebra with weight zero. The deformation and O-operator of
differential 3-Lie algebras are also investigated. Finally, we consider abelian
extensions of differential 3-Lie algebras.
