Abstract
This article is concerned with the Hartree equations with harmonic potential. By an elaborate mathematical analysis, we obtain a sharp stability threshold of this equation. Then with this threshold, we prove that the standing wave of this equation exists and is stable.
Acknowledgements
This project is supported by the National Science Foundation of China (Grant Nos. 10771151, 10901115 and 11126335), the Scientific Research Fund of Sichuan Provincial Education Department (Grant No. 10ZB003), and the Scientific Research Fund of Sichuan Provincial Science, Technology Department (Grant No. 2010JY0057) and Sichuan Province Science Foundation for Youths (Grant No. 2012JQ0011).