A Shooting Approach to Layers and Chaos in a Forced Duffing Equation

We study equilibrium solutions for the problem Using a shooting method we find solutions for all nonzero . For small we add to the solutions found by previous authors, especially Angenent, Mallet-Paret and Peletier, and Hale and Sakamoto, and also give new elementary ode proofs of their results. Among the new results is the existence of internal layer-type solutions. Considering the ode satisfied by equilibria, but on an infinite interval, we obtain chaos results for and . We also consider the problem of bifurcation of solutions as λ increases.