ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

9. Ordinary Differential Equations and Dynamical Systems

1991 MS Classification: 34 Mehri, Bahman, Sharif University of Technology, Tehran, Iran On the existence of periodic solutions for nonlinear ODE

We consider the nth order differential equation x^{(n)} + ∑_{i=0}^{n−1} g (x^{(i−1)}) x^{(i)} +

f(x, x′, …, x^{(n−1)}) = e(t). Under certain conditions on the nonlinear terms g and f, the existence of a periodic solution is obtained. This work is a generalization Reissig’s result on a third order equation of the same type. Reference: R. Reissig, An extension of Ezeilo’s result, Annali di Mathematica Pura Appl. 14 (1971), 199–209.