Ważewski’s method for systems of dynamic equations on time scales Original Research Article

In the paper the Ważewski’s method, which is well-known for ordinary differential equations, is developed for a system of dynamic equations on an arbitrary time scale. Sufficient conditions guaranteeing the existence of at least one solution with a graph staying in a previously defined open set are derived. This result, generalizing some previous results concerning the asymptotic behavior of solutions of discrete equations, is suitable for investigating of asymptotic behavior of solutions of dynamical systems. A relevant example is considered.