ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

9. Ordinary Differential Equations and Dynamical Systems

1991 MS Classification: 34 Shadman, Dariush, Department of Mathematics, Sharif University of Technology, Tehran, Iran On the boundedness of the solutions of a certain nth order ODE We are concerned with the behavior of the solutions of the nth order dif-

ferential equation x^{(n)} + ∑_{i=0}^{n−1} p_{i}(t)f_{i} (x^{(i)}) = g(t), where the functions p_{i}, f_{i}

and g satisfy certain smoothness conditions. With the aid of some auxiliary functions an energy function is constructed, from which boundedness and other properties of the solutions are deduced. Reference: M. S. Zarghami and B. Mehri, On the behavior of certain third order differential equation, J. London Math. Soc. (2), 4 (1971), 271–276.