Birkohoff theory for non-autonomous differential equations with delay

讨论无穷时滞泛函微分方程非线性振动性的方法有很多。动力系统对于具有唯一性的方程是非常重要的。另一种方法是分析方法。分析方法是非常困难的，因为对于相空间的维数为无穷大或无穷大的情形有很多方法，本文只考虑解的性质，称为过程。这个想法是由拉萨尔不变原理的主要所在地布朗大学提出的。对于上述问题，我们有以下几个结果：（1）在泛函微分方程和发展方程中的应用。(ii)偏微分方程的应用。(iii)一般动力系统的构造（iv）动力系统最佳拓扑的构造，从而可以讨论许多结果。

There are many methods to discuss nonlinear oscillations for functional differential equations with infinite delay. Dynamical systems are very important for equations with uniqueness property. Another methods are analytic methods. Analytic methods are very difficult, because there are many methods for the case the dimension of phase spaces is infinite or infinite.In this reports, we consider the only the property of solutions which is called processes. This idea is based by Brown University that is the main place of LaSalle's invariant principle. We have the followings for the above problem: (i) Application to functional differential equations and evolution equations. (ii) Applicaions to partial differential equations. (iii) Construction of general dynamical systems (iv) Construction of the best topology for dynamical systems.Thus we could discuss many results.