Asymptotic and Periodic Boundary Value Problems of Mixed FDEs and Wave Solutions of Lattice Differential Equations

We discuss the existence and approximation of solutions of asymptotic or periodic boundary value problems of mixed functional differential equations. Our approach is via monotone iteration and non-standard ordering in the profile set for asymptotic boundary value problems and viaS1-degree and equivariant bifurcation theory for periodic boundary value problems. Applications will be given to wave fronts and to slowly oscillatory spatially periodic traveling waves of lattice delay differential equations arising from population genetics, population dynamics, and neural networks.