Lagrangian Stability of a Class of Second-Order Periodic Systems

We study the following second-order differential equation: [inline-graphic not available: see fulltext], where [inline-graphic not available: see fulltext]  ([inline-graphic not available: see fulltext]), [inline-graphic not available: see fulltext] and [inline-graphic not available: see fulltext] are positive constants, and [inline-graphic not available: see fulltext] satisfies [inline-graphic not available: see fulltext]. Under some assumptions on the parities of [inline-graphic not available: see fulltext] and [inline-graphic not available: see fulltext], by a small twist theorem of reversible mapping we obtain the existence of quasiperiodic solutions and boundedness of all the solutions.