高阶微分方程的周期解及多重性

项目名称： 高阶微分方程的周期解及多重性

项目编号： No.11501240

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 梁树青

作者单位： 吉林大学

项目金额： 18万元

中文摘要： 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。

中文关键词： 周期解；存在性；多重性；Floquet；theory

英文摘要： 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.

英文关键词： periodic solutions;existence;multiplicity;Floquet theory