Geodesic
Ultimate boundedness results for solutions of certain third order nonlinear matrix differential equations
Kragujevac Journal of Mathematics, Tome 33 (2010) no. 1.

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We present in this paper ultimate boundedness results for a third order nonlinear matrix differential equations of the form $$t{...}{X}+Aḍot{X}+B\dot{X}+H(X)=P(t,X,\dot{X},ḍot{X}),$$ where $A, B$ are constant symmetric $n\times n$ matrices, $X, H(X)$ and $P(t,X,\dot{X},\ddot{X})$ are real $n\times n$ matrices continuous in their respective arguments. Our results give a matrix analogue of earlier results of Afuwape [1] and Meng [4], and extend other earlier results for the case in which we do not necessarily require that $H(X)$ be differentiable. 
@article{KJM_2010_33_1_a6,
     author = {M. O. Omeike and A. U. Afuwape},
     title = {Ultimate boundedness results for solutions of certain third order nonlinear matrix differential equations},
     journal = {Kragujevac Journal of Mathematics},
     pages = {83 - 94},
     publisher = {mathdoc},
     volume = {33},
     number = {1},
     year = {2010},
     url = {http://geodesic.mathdoc.fr/item/KJM_2010_33_1_a6/}
}
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M. O. Omeike; A. U. Afuwape. Ultimate boundedness results for solutions of certain third order nonlinear matrix differential equations. Kragujevac Journal of Mathematics, Tome 33 (2010) no. 1. http://geodesic.mathdoc.fr/item/KJM_2010_33_1_a6/