Ultimate Boundedness of Solutions of Some System of Third-Order Nonlinear Differential Equations

Abstract

This paper presents sufficient conditions for the ultimate boundedness of solutions of some system of third-order nonlinear differential equationswhere Ψ, Φ are positive definite symmetric matrices, H, P are n-vectors continuous in their respective arguments, X ∈ R n and t ∈ R + = [0, +∞).We do not necessarily require H(X) differentiable to obtain our results.By using the Lyapunov's direct (second) method and constructing a complete Lyapunov function, earlier results are generalized.