Mathematical Sciences: Non-autonomous Differential Equations

这个项目的目标是发展和应用有助于研究非线性非自治微分方程解的存在性、多解性和稳定性的拓扑和分析方法。这些方程是被迫的，或者具有时间依赖性，这一事实使它们变得相当复杂。微分方程组的强迫模型是日常生活中出现的各种各样的现象。共振附近的非线性问题非常复杂，需要非常复杂的数学才能给出定性信息。

The goal of this project is the development and application of topological and analytical methods useful for the study of existence, multiplicity, and stability of solutions of nonlinear nonautonomous differential equations. The fact that the equations are forced or have temporal dependence complicates them considerably. Differential equations with forcing model a wide variety of phenomena that occurs in everyday life. Problems with nonlinearities near resonance are very complicated and require very sophisticated mathematics to give qualitative information.