where we agree to interpret x ~ as x n. [As there will be a frequent need to make such interpretat ions, due to the cyclic nature of the feedback in (0.1), let us agree that all indices… (More)

We consider cyclic nearest neighbor systems of di erential delay equations, in which the coupling between neighbors possesses a monotonicity property. Using a discrete (integer-valued) Lyapunov… (More)

We prove a Fredholm alternative theorem for a class of asymptotically hyperbolic linear di erential di erence equations of mixed type. We also establish the cocycle property and the spectral ow… (More)

We obtain existence of traveling wave solutions for a class of spatially discrete systems, namely lattice di erential equations. Uniqueness of the wave speed c, and uniqueness of the solution with c… (More)

We de ne a discrete (integer-valued) Lyapunov function V for cyclic nearest neighbor systems of di erential delay equations possessing a feedback condition. This extends analogous de nitions for… (More)

We consider in nite systems of ODE's on the two-dimensional integer lattice, given by a bistable scalar ODE at each point, with a nearest neighbor coupling between lattice points. For a class of… (More)

We consider an array of scalar nonlinear dynamical systems _ u = f(u), arranged on the sites of a spatial lattice, for example on the integer lattice ZZ2 in the plane IR2. We impose a coupling… (More)

We illustrate that most existence theorems using degree theory are in principle relatively constructive. The first one presented here is the Brouwer Fixed Point Theorem. Our method is "constructive… (More)

We study the nonlinear eigenvalue problem f(x) = λx for a class of maps f : K → K which are homogeneous of degree one and order-preserving, where K ⊆ X is a closed convex cone in a Banach space X.… (More)

If L : Y → Y is a bounded linear map on a Banach space Y , the “radius of the essential spectrum” or “essential spectral radius” ρ(L) of L is well-defined and there are well-known formulas for ρ(L)… (More)