Boundedness of solutions of second order differential equations

1974 ◽  
pp. 67-70
Author(s):  
M. L. Cartwright
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Boundedness Of Solutions ◽  
Second Order Differential Equations

scholarly journals Boundedness of Solutions for Second Order Differential Equations

2020 ◽  
Vol 12 (4) ◽  
pp. 58
Author(s):  
Daniel C. Biles
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Differential Equations ◽  
Boundedness Of Solutions ◽  
Second Order Differential Equations ◽  
All Solutions ◽  
Non Linear ◽  
Linear Differential

We present new theorems which specify sufficient conditions for the boundedness of all solutions for second order non-linear differential equations. Unboundedness of solutions is also considered.

scholarly journals Boundedness of Certain System of Second Order Differential Equations

2021 ◽  
Vol 45 (5) ◽  
pp. 787-796
Author(s):  
M. O. OMEIKE ◽  
◽  
A. A. ADEYANJU ◽  
D. O. ADAMS ◽  
A. L. OLUTIMO
Keyword(s):  
Lyapunov Function ◽  
Differential Equations ◽  
Second Order ◽  
System Of Equations ◽  
Boundedness Of Solutions ◽  
Ultimate Boundedness ◽  
Basic Technique ◽  
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 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.

Banach Lie Algebroids

2011 ◽  
Vol 57 (2) ◽  
pp. 409-416
Author(s):  
Mihai Anastasiei
Keyword(s):  
Differential Equations ◽  
Smooth Manifold ◽  
Vector Bundles ◽  
Second Order ◽  
Lie Algebroids ◽  
Second Order Differential Equations

Banach Lie AlgebroidsFirst, we extend the notion of second order differential equations (SODE) on a smooth manifold to anchored Banach vector bundles. Then we define the Banach Lie algebroids as Lie algebroids structures modeled on anchored Banach vector bundles and prove that they form a category.

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