Synthetic study of nonlinear evolution equation and its related topics

从非线性发展方程理论的角度，综合运用非线性泛函分析理论、实变函数理论、常微分方程组理论和变分理论，对物理和工程中出现的各种类型的非线性偏微分方程组(非线性椭圆型方程、非线性扩散方程、非线性波动方程、非线性薛定谔方程)进行了综合研究。

Various types of nonlinear PDEs (nonlinear elliptic equations, nonlinear diffusion equations, nonlinear wave equations, nonlinear Schrodinger equations) arising in physics and engineering were synthetically studied from the viewpoint of the theory of nonlinear evolution equations by using the techniques from the theory of nonlinear functional analysis, the theory of functions of a real variable, the theory of ordinary differential equations and the calculus of variations.