UNIFORM ULTIMATE BOUNDEDNESS RESULTS FOR SOME SYSTEM OF THIRD ORDER NONLINEAR DELAY DIFFERENTIAL EQUATIONS

. The paper is concerned with the study of the uniform ultimate boundedness of solutions of the third-order system of nonlinear delay differential equation where A, B are real n x n constant symmetric matrices, r is a positive real constant and X E In, using the Lyapunov-Krasovskii functional method and following the arguments used in [1] and [10], we obtained results which give an n-dimensional analogue of an earlier result of [13] and extend other earlier results for the case in which we do not necessarily require that H(X (t - r)) be differentiable.