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

Abstract

Abstract 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 −ü − μu + g(t)h(u) = 0 where μ > 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 Schrödinger equation