研究半线性椭圆型方程和方程组。利用临界点理论和现代偏微分方程方法，对非线性椭圆型方程解的存在性、多解性和渐近性，得到了一系列有趣的结果。特别低，解决和部分解决了半线性椭圆方程中的2个公开问题。

In this paper, we focus on semilinear elliptic equations and systems. Using the critical point theory and the modern PDE methods, we obtained a series of interesting results on the existence, multiplicity and the asymptotic behavior of solutions for nonlinear elliptic equations. In particular, we solved or partially solved two open problems in semilinear elliptic equations.