An existence theorem for harmonic solutions of periodically perturbed systems of Duffing’s type. (English) Zbl 0757.34032

By use of topological index the author proves an existence theorem for Duffing’s system with positive damping, \(x''+Cx'+\text{grad} G(x)=p(t)\), under the conditions (1) \((Cy,y)\geq a(y,y)\), for every \(y\) in \(\mathbb{R}\), with constant \(a>0\); (2) \((x,\text{grad} G(x))\geq b(x,x)\), for \(| x|>d\) with constants \(b>0\) and \(d>0\).


34C25 Periodic solutions to ordinary differential equations
34D10 Perturbations of ordinary differential equations