Periodic solutions of the third-order differential equation with right- hand side in the form of nonlinear restoring term plus general gradient- like part. (English) Zbl 0777.34029

The nonlinear differential equation \((*)\) \(x'''=h(x)+[f(t,x,x']'\) is considered. In \((*)\), \(h\in{\mathcal C}(\mathbb{R}^ 1)\), \(f\in{\mathcal C}^ 1(\mathbb{R}^ 3)\) and \(f\) is \(T\)-periodic in \(t\). Results about \(T\)-periodic solutions of \((*)\) are obtained: namely sufficient conditions for the existence of a harmonic solution are worked out.


34C25 Periodic solutions to ordinary differential equations
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