Properties of solutions of some forced nonlinear oscillators at resonance (Q2711945)

This article surveys some recent results on the existence of periodic solutions, unbounded solutions and the boundedness of the set of solutions of bounded nonlinear perturbations of periodically forced resonant linear or asymmetric oscillators. Among the ordinary differential equations considered are NEWLINE\[NEWLINEu''(t)+n^2 u(t)=e(t),NEWLINE\]NEWLINE where \(n\) is a nonnegative integer and \(e\) a \(2\pi\)-periodic continuous function, NEWLINE\[NEWLINEu''(t)+ n^2u(t)= f\bigl( u(t) \bigr)+e(t),NEWLINE\]NEWLINE where \(f\) is continuous and bounded, and NEWLINE\[NEWLINEu''(t)+ \mu u^+(t)- \nu u^-(t)= e(t),NEWLINE\]NEWLINE where \(\mu,\nu\) are positive numbers, \(u^+=\max \{u,0\}\) and \(u^-=\max \{-u,0\}\).NEWLINENEWLINEFor the entire collection see [Zbl 0959.00021].