Hartree和Hartree－Fock极小问题解的存在性

THE EXISTENCE OF HARTREE AND HARTREE-FOCKMINIMIZATION PROBLEMS

应用集中紧致原理，在Ｌｉｏｎｓ研究Ｈａｒｔｒｅｅ和Ｈａｒｔｒｅｅ－Ｆｏｃｋ方程组多解存在性的基础上对Ｈａｒｔｒｅｅ和Ｈａｒｔｒｅｅ－Ｆｏｃｋ极小问题作了进一步研究．给出了保证Ｈａｒｔｒｅｅ和Ｈａｒｔｒｅｅ－Ｆｏｃｋ极小可达的充分条件，同时部分回答了Ｌｉｏｎｓ提出的一个开问题．

in this paper, we use the concentration-compactness principle to studyHartree and Hartree-Fock minimization problems. We give a sufficient condition forthe existence of Hartree and Hartree-Fock minimization problems. At the sametime, we answer the open problem in the paper [5].