Lyapunov vector functions and partial boundedness of solutions with partially controlled initial conditions

Abstract

On the basis of the method of Lyapunov vector functions, we obtain a sufficient test for the uniform partial boundedness of solutions with partially controlled initial conditions. We introduce the notions of partial equiboundedness, partial equiboundedness in the limit, and partial uniform boundedness in the limit of solutions with partially controlled initial conditions. By the method of Lyapunov vector functions, we obtain sufficient tests for the partial equiboundedness of solutions and for the partial uniform boundedness in the limit and partial equiboundedness in the limit of solutions with partially controlled initial conditions.