Boundedness of Certain System of Second Order Differential Equations
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Authors: M. O. OMEIKE, A. A. ADEYANJU, D. O. ADAMS AND A. L. OLUTIMO
DOI: 10.46793/KgJMat2105.787O
Abstract:
This work is concerned with the ultimate boundedness of solutions of the system of vector differential equations
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where t ∈ ℝ+, X = X(t), Y = Y (t) ∈ ℝn, F : ℝn × ℝn → ℝn×n, G,H : ℝn → ℝn and P : ℝ+ × ℝn × ℝn → ℝn. By using a Lyapunov function as a basic technique, we prove that the solutions of the system of equations are ultimately bounded. In addition, result obtained includes and improves some related results in literature.
Keywords:
Boundedness, Lyapunov function, differential equations of second order.
References:
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