Ultimate boundedness results for solutions of certain third order nonlinear matrix differential equations (2010)
ABSTRACT: We present in this paper ultimate boundedness results for a third order nonlinear matrix differential equations of the form ...X +AX¨ + BX˙ + H(X) = P(t, X, X, ˙ X¨), where A, B are constant symmetric n × n matrices, X, H(X) and P(t, X, X, ˙ X¨) are real n×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.