本项目主要研究高阶微分方程与方程组周期解的多重性与稳定性。二阶常微分方程周期解的存在性、多重性与稳定性已有广泛研究。而有关高阶微分方程周期解的多重性与稳定性的研究成果还很少。部分原因是高阶微分方程或方程组的近似方程与二阶非线性方程的近似方程有明显区别，后者的谱分析结果丰富，如Floquet理论以及Hill方程的旋转数刻画方法，而前者的谱分析结果较少。本项目将分析一类线性化算子的谱，进而研究高阶微分方程与方程组的周期解的多重性以及稳定性。

The aim of this project is to study the existence, multiplicity and stability of higher order differential equations and the systems of differential equations. There are a lot of results about the existence, multiplicity and stability of second order differential equations. Could we give some results for higher order differential equations and the systems of differential equations for a class of nonlinearity? There are many researches for the spectrum for second order differential equations, such as Floquet theory and rotation numbers, periodic and anti-periodic eigenvalues. However, the research for the spectrum for higher order differential equations and the systems of differential equations is small. The spectrum for higher order differential equations will be studied, and then multiplicity and stability of higher order differential equations and the systems of differential equations will be studied.