Harmonic solutions of some second order nonlinear equations under a periodic force (Q1074749)

By use of geometrical methods, the author discusses the existence of harmonic solutions for second order nonlinear equations such as \[ (1)\quad \ddot x+f(x)\dot x+g(x)=p(t);\quad (2)\quad \ddot x+f(x,\dot x)\dot x+g(x)=p(t);\quad (3)\quad \ddot x+F(\dot x)+g(x)=p(t) \] where \(p(t+T)=p(t)\). The main results generalize relevant propositions of S. Lefshitz, De Castro, S. Mizohata and M. Yamaguti, etc.