Well-posedness of Cauchy problem of fourth-order Schrödinger equations in anisotropic Sobolev space

We study the existence of solutions for the Cauchy problem of the non-isotropically perturbed nonlinear Schrödinger equation iut+Δu+a∑i=1duxixixixi+|u|αu=0, where a is a real number, a≠0, α is a positive constant, 1⩽d