On a boundedness condition for solutions of a generalized Liénard equation (Q1088046)

A Liénard type system \[ (1)\quad x'=y-f(x)+p(t),\quad y'=-g(x) \] is considered, where f,g are locally Lipschitz continuous in \({\mathbb{R}}\) and p is bounded and piecewise absolutely continuous in [0,\(\infty)\). The main theorems give conditions on f,g,p for the solutions of (1) to be uniformly bounded, uniformly ultimately bounded, or unbounded. Also a uniform boundedness theorem is obtained for a vector analogue of (1).