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
under periodic boundary conditions. As a result, the existence of a Whitney smooth family of small-amplitude reducible quasi-periodic solutions is obtained.
Given a list assignment of L to graph G, assign a list L(v) of colors to each