本项目拟研究几类二阶Hartree方程和分数阶Hartree方程，我们将从以下几个方面展开研究：1.孤立奇性的分类；2.找出Hartree非线性项的临界指数曲线，使得半线性Hartree椭圆问题在次临界条件下存在奇性解；3.讨论奇性解的唯一性、正则性、对称性和渐近性态。我们希望通过对Hartree方程的研究，可以揭示非局部非线性项与微分算子对解奇性的影响，丰富泛函分析和偏微分方程理论。

In this project, we study some second order Hartree equations and fractional Hartree equations. We will study from the following aspects: 1. the classification of isolated singularities; 2. finding out the critical exponential curve of Hartree nonlinear term, such that the semilinear Hartree elliptic problem has singular solution under subcritical condition; 3. the uniqueness, regularity, symmetry and asymptotic behavior of singular solutions. We hope that the study of Hartree problems reveals how the nonlocal nonlinearity and the differential operator work on the solutions’ singularities and enrich the basic theories of functional analysis and partial differential equations.