Estimates for the number of forced periodic oscillations in nonlinear systems (Q1594197)

The author studies nonautonomous differential systems of the types \((*)\) \(dy/dt = f(t,y)\) and \((**)\) \(-y''(t)=g(t,y,y').\) Using inclusions of the kind \(\alpha_j (y_j) < f_j (t,y), g_j (t,y,\bar{y}) < \beta_ j (y_j),\) lower estimates for the number of harmonic solutions to \((*)\) and \((**)\) are derived.