Birkohoff theory for non-autonomous differential equations with delay

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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.