Invariant tori and boundedness in asymmetric oscillations.
This paper deals with the boundedness of all solutions of the equation \[ x''+ ax^+- bx^-+ \varphi(x)= p(t),\tag{1} \] where \(p(t)\) is a smooth periodic function, \(a\) and \(b\) are positive constants, and the perturbation \(\varphi(x)\) is bounded. The analysis for (1) is based on standard technique related to KAM theory.
scientific article; zbMATH DE number 2032511