In this paper, we study non-abelian extensions of 3-Leibniz algebras through Maurer-Cartan elements. We construct a differential graded Lie algebra and prove that there is a one-to-one correspondence between the isomorphism classes of non-abelian extensions in 3-Leibniz algebras and the equivalence classes of Maurer-Cartan elements in this differential graded Lie algebra. And also the Leibniz algebra structure on the space of fundamental elements of 3-Leibniz algebras is analyzed. It is proved that the non-abelian extension of 3-Leibniz algebras induce the non-abelian extensions of Leibniz algebras.

In this paper, we prove an infinite dimensional KAM theorem and apply it to study 2-dimensional nonlinear Schrödinger equations with different large forcing terms and (2p + 1)-nonlinearities

　　　　　 \mathrm{i}{u}_t-\mathrm{\Delta }u+{\phi }_1\left({\overline{\omega }}_{1}t\right)u+{\phi }_2\left({\overline{\omega }}_{2}t\right)|u{|}^{2p}u=0,t\in \mathbb{R},x\in {\mathbb{T}}^2

under periodic boundary conditions. As a result, the existence of a Whitney smooth family of small-amplitude reducible quasi-periodic solutions is obtained.