非线性奇异椭圆型偏微分方程是自然界突变现象的数学模型，比如流体力学中的边界层现象，冰山的移动等自然现象中都出现了这种模型。为解决实际应用中产生的问题，我们需要对该类型方程进行系统的研究。我们前期的工作建立了针对小于-1指数的奇异型偏微分方程基本模型及复杂非线性情形，例如矩阵型和Kirchhoff型强奇异偏微分方程的可解性理论。在这些基础上我们计划进一步研究强奇异微分方程在无穷远处超线性增长情形下能量有限解存在性以及有singular potential的强奇异偏微分方程解的奇点研究。希望得到一些更精细的结果，进而推动相关领域的发展。闵可夫斯基问题是凸几何分析的核心问题之一，我们将进一步研究复杂的Orlicz闵可夫斯基问题。

Fluid dynamicists have long known the appearance of boundary layers in which nonlinear singular elliptic equations arise. Since then much attention has been paid upon non-differential functionals and singularity. Our previous work have established an optimal condition for the existence of solutions with finite energy (ie,H_0^1-solutions) for strongly singular problems (ie,-p<-1), which has been applied to Kirchhoff type strongly singular equations et al. Then we shall study the property of solutions for strongly singular problems with singular potentials and the combined effect of strongly singularity and super-linear nonlinearity. The Minkowski problem is one of the central problems in convex geometric analysis. We shall continue our study for Orlicz Minkowski problem proposed by Haberl et al.in 2010.