On the continuous dependence on parameters of solutions of the second order periodic problem (Q1840635)

Sufficient conditions are established under which the second-order problem \[ \ddot u=\nabla F(t,u,\omega),\quad u(0)-u(T)=\dot u(0)-\dot u(T)=0, \] has solutions which continuously depend on the parameter \(\omega\). \(F\) is assumed to be convex and such that \(\nabla F\) is bounded.