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

Cemil, Tunç

Appl. Math. Mech., Engl. Ed. 20, No. 2, 163-170 (1999).

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).

Reviewer: I.Foltyńska (Poznań)

MSC:

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

Keywords:

nonlinear differential equations; ultimate boundedness; solutions; existence; periodic solutions

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