On the Periodic Solution to the Newtonian Equation of Motion

Consider the system of ordinary differential equation u”(t)+grad G(u(t))=p(t),(1)where p:R→R”is continuous and 2π periodic and G:R~π→R has continuous secondorder partial derivatives.The system can be interpreted physically as the Newto-nian equation of motion of a mechanical system subject to conservative internalforces and the periodic external forces.