Large-amplitude subharmonic oscillations for scalar second-order differential equations with asymmetric nonlinearities (Q1327081)

The second-order differential equation (1) \(\ddot u(t) + g(t,u(t)) = 0\), where \(g(t,u(t))\) is \(T\)-periodic with respect to its first variable is considered. It is assumed that the nonlinearity may have a different behaviour to the left and to the right of the origin. The existence of subharmonic solutions of (1) is studied. Some careful estimates on the critical levels of mountain pass and saddle point type of the associated functional are employed. Sufficient conditions for existence of subharmonic solutions of (1) are given.