Existence of Weak and Strong Solutions of Nonlinear Differential Equations with Delay in Banach Space

Existence of weak and strong solutions of nonlinear differential equations with delay in Banach space is discussed. In the present work we give a generalization to recent results. We prove that, with certain conditions, every nonlinear differential equation with delay has at least one weak solution, furthermore, under suitable assumptions, these equations have solutions. Next under a generalization of the compactness assumptions, we show the same equations have solutions too.