【摘要】 研究一类带双势的非线性Schr dinger方程.通过对势函数V(x)和K(x)作适当假设,运用能量方法和一些先验估计式,得到了该Schr dinger方程初值问题的解在有限时间内坍塌的充分条件为E(0)<0x0 0dx [2E(0)∫RNx0 0dx>0或E(0)>0,hIm∫RN或E(0)=0,h2Im∫RN｜x｜2｜0｜2dx]12.更多还原

【Abstract】 This paper is concerned with a class of nonlinear Schrdinger equations with double potentials. Under suitable assumptions on potential functions V（x） and K（x）, using energy method and some prior estimates, we prove that the following conditions are sufficient for the solution of the initial value problem of the Schrdinger equation to blow up in a finite time:E（₀）<0 or E（₀）=0,h²Im∫_R^Nx₀（₀）dx>0 or E（₀）>0,hIm∫_R^Nx₀（₀）dx[2E（₀）∫_R^N|x|²|₀|²dx]¹².更多还原