Contributions à l'étude de l'existence des solutions presque périodiques et presque automorphes pour des systèmes dynamiques en dimension infinie, applications à des équations différentielles non locales en temps

Abstract

In this thésis, we have investigated the existence of Cn-almost periodic or Cn-almost automorphic solutions for partial functional equations of retarded an neutral type in banach spaces. In the whole of the thesis, we used the Massera's approach. We proved the mains results of this thesis under optimal conditions, namely, we showed that the existance of a bounded solution for retared or neutral systems.The technics we used is based on the reduction principle method which reduces the complexity of systems from infinite to finite dimention. In fact, the existence of Cn_almost periodic or Cn-almost automorphic solutions for partial functional differential equations is reuced to the existence of Cn-almost periodic or Cn-almost automorphic solution for nonhomogeneous ordinary differential equation in Rd. We plan to develop and to improve the results of this thesis for more general dynamical systems.