An Example of Chaos for a Cubic Nonlinear Schrodinger Equation with Periodic Inhomogeneous Nonlinearity

Using a topological approach we prove the existence of infinitely many periodic solutions, as well as the presence of symbolic dynamics for second order nonlinear differential equations of the form -u - mu u + g(t)h(u) = 0 where mu > 0 is a given constant and g : R -> R is a periodic positive weight function. Our main application concerns the study of the case in which h(u) is a cubic nonlinearity. Such a choice is motivated by previous investigations dealing with the nonlinear Schrodinger equation i psi(t) = -1/2 psi(xx) + g(x)vertical bar psi vertical bar(2)psi.