Functional differential equations of delay type and nonlinear evolution in Lp-spaces

AbstractNonlinear nonautonomous functional differential equations of delay type with Lp-initial functions is studied by means of the theory of evolution operators in Lp-spaces. Using the evolution operator in C it is shown that the evolution operator constructed in Lp × Rn determines the solutions of the initial value problem in the exact sense. A variation of parameters formula is developed for the nonlinear perturbed equation