On the stability and boundedness of solutions of some nonlinear differential equations of fourth and fifth-order with delay
by
Cemil Tunc
Department of Mathematics, Faculty of Arts and Sciences, Yuzuncu Yil University, 65080, Van - Turkey

In the present paper, sufficient conditions are established to ensure the asymptotic stability of zero solution of a certain nonlinear differential equation of fourth order with delay and the boundedness of all solutions of a certain nonlinear differential equation of fifth order with delay. By introducing Lyapunov functionals, we obtain two new results on the subject. To the best of our knowledge in the relevant literature, in spite of the existence of a few papers on the boundedness of solutions of fifth order nonlinear differential equations without delay, it was not found any paper on the same topic for fifth order nonlinear differential equations with delay.

Date received: November 30, 2006