On differential equations with delay in Banach spaces and attractors for retarded lattice dynamical systems (Q379690)

The aim of this work is to study the existence of solutions for some differential equations in a Banach space E with delay. Here, the authors use a new approach based on the weak topology. The nonlinear part is not assumed to be continuous using the topology of uniform convergence, the authors assume only that it is weakly continuous. Firstly, the authors define a weak convergence in the space of initial date and prove the existence of solution when E is reflexive and separable, then they prove by an approximation approach that the solution exists and satisfies the equation almost everywhere. After that, the authors prove the existence of a global attractor.