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摘要
In this paper, we consider the nonlinear Schrodinger equation iu(t) + Delta u +theta(omega t) vertical bar u vertical bar(alpha)u = 0 in R(N) where alpha is an H(1)-subcritical exponent and theta is a periodic function. We show that, for a given initial condition u(t(0)) = phi epsilon H(1)(R(N)), the solution u converges as |omega| -> infinity to the solution of the limiting equation iU(t) + Delta U + I (theta)| U|alpha(U) = 0 with the same initial condition, where I (theta) is the average of theta. We also show that if the limiting solution U is global and has a certain decay property as t ->infinity, then u is also global if |omega| is sufficiently large.
- 出版日期2010-7
