Boundedness of Certain System of Second Order Differential Equations

This work is concerned with the ultimate boundedness of solutions of the system of vector differential equations X˙ = H (Y ), Y˙ = − F (X, Y )Y − G (X ) + P (t,X, Y ), 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...

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Veröffentlicht in:Kragujevac Journal of Mathematics 2021, Vol.45 (5), p.787-796
Hauptverfasser: OMEIKE, M. O., ADEYANJU, A. A., ADAMS, D. O., OLUTIMO, A. L.
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Sprache:eng
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Zusammenfassung:This work is concerned with the ultimate boundedness of solutions of the system of vector differential equations X˙ = H (Y ), Y˙ = − F (X, Y )Y − G (X ) + P (t,X, Y ), 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.
ISSN:1450-9628
2406-3045
DOI:10.46793/KgJMat2105.787O