UNIFORM ULTIMATE BOUNDEDNESS OF SOLUTIONS OF THIRD-ORDER NONLINEAR DELAY DIFFERENTIAL EQUATIONS

In this paper, we study the uniform boundedness. and uniform ultimate boundedness of solutions of the third-order delay differential equation (*) (x) triple over dot + phi(x, (x) over dot)x + g((x) over dot(t - r(t)) + f(x(t - r(t)) = p(t, x, (x) over dot, x) where 0 <= r (t) <= gamma,gamma is a positive constant, phi(x, (x) over dot)), g((x) over dot)), f(x) and p(t, x, (x) over dot), x) are continuous functions. We obtain some sufficient conditions which ensure that all the solutions of Eq.(*) are uniformly bounded and uniformly ultimately bounded. Our result revise and improve some earlier results.