方程iu_t=-Δu-k(x)|u|^(p-1)u的爆破性质

The Blow-up Properties for Equations iu_t=-Δu-k(x)|u|^(p-1)u

研究一类非线性Schr dinger方程iut=-Δu-k(x)｜u｜p-1u的初值问题,其中k(x)为Rn上的有界可微函数,当n 3时,1+4n-2;当n=2时,3 p<+∞.使用推广的能量方法讨论了该n p<n+2方程初值问题的爆破性质.

In this paper, we consider the Cauchy problems of a class of nonlinear Schrdinger equations iut=-Δu-k(x)|u|p-1u, where k(x) is a bounded and differentiable function on Rn. For the equation,we only consider 1+4np<n+2n-2 for n3 and 3p<+∞ for n=2. By using the developed energy method, we study the blowup properties for the Cauchy problem of the equation.