On the boundedness and periodicity of the solutions to a certain vector differential equation of third-order. (English) Zbl 0933.34058

The third-order system of nonlinear differential equations \[ \dddot X+F(X,\dot X)\ddot X+B\dot X+H(X)=P(t,X,\dot X,\ddot X)\tag{1} \] is considered, with \(X\in\mathbb{R}^n\), \(F,H\) and \(P\) are continuous, \(B\) is a real constant symmetric \(n\times n\)-matrix and the dots denote differentiation with respect to \(t\).
Sufficient conditions are established for the ultimate boundedness of solutions and for the existence of periodic solutions to (1).


34D40 Ultimate boundedness (MSC2000)
34C25 Periodic solutions to ordinary differential equations
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