Positive periodic solutions of second order nonlinear equations with indefinite weight: Multiplicity results and complex dynamics

We prove the existence of a pair of positive T -periodic solutions as well as the existence of positive subharmonic solutions of any order and the presence of chaotic-like dynamics for the scalar second order ODE u +aλ,μ(t)g(u) = 0, where g(x) is a positive function on R +, superlinear at zero and sublinear at infinity, and aλ,μ(t) is a T -periodic and sign indefinite weight of the form λa+ (t)−μa− (t), with λ,μ > 0 and large.