The global solution of anisotropic fourth-order Schrodinger equation

This paper studies the global existence of solutions in Sobolev space for anisotropic fourth-order Schrodinger type equation: iu(t)+Delta u+a Sigma(d)(i=1)=1(u)x(i)x(i)x(i)x(i)+b vertical bar u vertical bar(alpha)u=0, x epsilon R-n, t epsilon R, 1 <= d<n under the initial conditions: u(x,0)=phi(x), x epsilon R-n. By using the Banach fixed point theorem, we obtain the existence, the uniqueness, the continuous dependence and the decay estimate of the solution on the initial value in anisotropic Sobolev spaces (H -> yH -> Zs2,r)-H-s1-H-1 rho.