中文摘要：

研究一类带调和势并具组合幂非线性项的非线性Schrodinger方程.该方程描述了在磁场势下具有相互吸引的Bose-Einstein凝聚.应用势井方法、凹方法和变分原理,给出了该方程Cauchy问题的整体解和爆破解存在的门槛条件.

英文摘要：

This paper is concerned with a class of nonlinear Schrodinger equations with combined power nonlinearities under a harmonic potential, which describes the attractive Bose-Einstein condensate under a magnetic trap. Originating in potential well method and concavity method, combining the variational argument, we obtain the sharp criteria of global existence and blowing up of the equation.