Equations with infinite delay: Blending the abstract and the concrete

Using perturbation theory for adjoint semigroups (a modification of sun-star calculus) we prove, in the case of infinite delay, the principle of linearized stability for nonlinear renewal equations, delay-differential equations and coupled systems of these two types of equations. Our results extend those of Diekmann et al. (1995) [13], and Diekmann et al. (2007) [14] to the case of infinite delay.