Ultimate boundedness results for a certain system of third-order non-linear differential equations

AbstractWe present in this paper ultimate boundedness results for a third-order system of non-linear differential equations of the form ·X + AẌ + B/.X + H(X) = P(t, X, /.X, Ẍ). where A, B are constant symmetric n × n matrices and X, H(X), P(t, X, X, X) are real n-vectors with H:Rn→Rn and P: R X RnX Rn X Rn X Rn → X Rncontinuous in their respective arguments. Our results give an n-dimensional analogue of an earlier result of Ezeilo in [1] and extend other earlier results for the case in which we do not necessarily require that H(X) be differentiable