On the boundedness and periodicity of the solutions to a certain vector differential equation of third-order
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).
scientific article; zbMATH DE number 1346265