Periodic solutions of a second order nonlinear system
The existence of periodic solutions of the Liénard system \[ x''(t)+ d[\text{grad }F(x(t))]/dt+ g(t,x(t))= e(t), \] where \(x\) is an \(n\)-dimensional vector and \(e(t)\) and \(g(t, x(t))\) are \(2\pi\)-periodic in \(t\), is investigated for various asymptotic behaviours of \(g\). Conditions for periodic solutions with detailed conditions are given in four theorems.
scientific article; zbMATH DE number 1115510
scientific article