Approximations of continuous periodic functions that are differentiable along the trajectories of dynamical systems (Q1090834)

Systems of autonomous differential equations are considered on the m dimensional torus with continuous right-hand side and uniqueness. A theorem is proved stating that under a generalized Lipschitz condition on the right-hand side any continuous function which is continuously differentiable along solutions of the system can be uniformly approximated in the \(C^ 1\) norm by continuously differentiable functions.