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摘要
We study the well-posedness for the Cauchy problem of the non-isotropically perturbed nonlinear Schrodinger equation iu(t) Delta u vertical bar u vertical bar(alpha)u a Sigma(d)(i=1) u(xixixixi) = 0, where a is a real constant, 1 <= d < n is an integer, alpha is a positive constant, and x = (x(1), x(2),..., x(n)) is an element of R-n. By using Kato's method, we establish some local and global existence results for initial data belonging to H-s(R-n), where s >= 0 if 0 < alpha <= 8/2n-d, s >= n/2 (1 - 8/(2n-d)alpha) if alpha >= 8/2n-d.
