中文摘要：

研究了宇宙常数是负值的Euler-Poisson方程,证明了一类爆破解的存在性（对应于物理上的中心塌缩现象）,并给出了具体的爆破速度;同时还证明了时间周期解的存在性.运用MATLAB数学软件对相关结果做了数值验证.

英文摘要：

Euler-Poisson system is an important model in physics,which describes the motion of a selfgravitating fluid in gaseous stars.This paper deals with the studies on the Euler-Poisson system with a cosmological negative constant.We have obtained the existence of blowup solutions（this fact is related to the core collapse phenomenon in physics）,given the detailed blowup rate,and also proved the existence of time periodic solutions for this system.By means of MATLAB,the results are tested numerically.