The symmetrization method and limit cycles of vibro-impact systems (Q945991)

The author studies systems \(\ddot x + p(x) \dot x + q(x) = 0\), in which \(x \geq 0\) denotes the position of an object in a line that has impact with a boundary at position 0. Subject to regularity conditions on \(p\) and \(q\) and reasonable conditions on the impacts, he states and proves a pair of theorems that imply existence of a limit cycle, and uniqueness of any limit cycle, for the corresponding system of first order differential equations.