On uniform-ultimate boundedness and periodicity results of solutions to certain second order non-linear vector differential equations
Keywords:second order, ultimate boundedness, periodicity, Lyapunov function
In this paper, we employ the second method of Lyapunov to examine sufficient conditions for the uniform-ultimate boundedness of solutions and existence of at least one periodic solution to the following second order vector differential equation:
Ẍ+ F(X, Ẋ ) Ẋ + H(X) = P(t, X, Ẋ ),
when the non-linear term H(X) is: (i) differentiable, (ii) non-necessarily differentiable. The results contain in this paper are new and complement related ones in the literature.
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