Ultimate Boundedness of Solutions of Some System of Third-Order Nonlinear Differential Equations
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Authors: A. A. ABDURASID, K. D. ADULOJU, M. T. RAJI, O. R. VINCENT AND M. O. OMEIKE
DOI: 10.46793/KgJMat2505.727A
Abstract:
This paper presents sufficient conditions for the ultimate boundedness of solutions of some system of third-order nonlinear differential equations
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where Ψ, Φ are positive definite symmetric matrices, H,P are n−vectors continuous in their respective arguments, X ∈ ℝn 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.
Keywords:
Ultimate boundedness, Lyapunov function, system of third-order nonlinear differential equations.
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