Uniform Boundedness in the Sense of Poisson of Solutions of Systems of Differential Equations and Lyapunov Vector Functions

We introduce several generalizations of the properties of equiboundedness and uniform boundedness of solutions of ordinary differential systems, which are united by the common names of equiboundedness in the sense of Poisson and uniform boundedness in the sense of Poisson. For each of the above-introduced properties, we use the method of Lyapunov vector functions to obtain sufficient criteria for the system to have a certain property. In terms of the upper Dini derivative of the Lyapunov function given by a system, several criteria are established for the solutions of this system to have the relevant type of uniform boundedness in the sense of Poisson.