Positive periodic solutions of second order nonlinear equations with indefinite weight: multiplicity results and complex dynamics (Q656194)

The authors 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 \[ u'' + a_{\lambda,\mu}(t)g(u)=0, \] where \(g(x)\) is a positive function on \(\mathbb R^+\), superlinear at zero and sublinear at infinity, and \(a_{\lambda,\mu}(t)\) is a \(T\)-periodic and sign indefinite weight of the form \(\lambda\) \(a^+(t)-\mu a^-(t)\), with \(\lambda, \mu>0\) and large.