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Boundedness of solutions of certain system of second-order ordinary differential equations. (English) Zbl 1321.34051

The authors consider the following second order non-linear system of differential equations \[ X'' + F(X,{X}'){X}' + H(X) = P(t,X,{X}'), \tag{1} \] where \(t \in \mathbb R^ + \), \(\mathbb R^ + = [0,\infty )\), \(X \in \mathbb R^n\), \(F\) is a continuous \(n\times n\)-symmetric matrix function, \(H:\mathbb R^n \to \mathbb R^n\) and \(P:\mathbb R^ + \times \mathbb R^n\times \mathbb R^n \to \mathbb R^n\) are continuous, and \(H\) is also differentiable with \(H(0) = 0\). They prove two new results on the boundedness of solutions of equation (1). By this work, the authors extend some known results, on the boundedness of certain second order nonlinear scalar differential equations to a system of differential equations of second order.

MSC:

34C11 Growth and boundedness of solutions to ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
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