Journal of Applied Mathematics and Stochastic Analysis
Volume 4 (1991), Issue 3, Pages 211-224
doi:10.1155/S1048953391000175
Stability of solutions of a nonstandard ordinary differential
system by Lyapunov's second method
Department of Mathematics, Sri Sathya Sai Institute of Higher Learning, Prasanthinilayam 515 134, Andhra Pradesh, India
Received 1 September 1990; Revised 1 December 1990
Copyright © 1991 M. Venkatesulu and P. D. N. Srinivasu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Differential equations of the form y′=f(t,y,y′) where f is not
necessarily linear in its arguments represent certain physical phenomena and
are known for quite some time. The well known Clairut's and Chrystal's
equations fall into this category. Earlier we established the existence of a
(unique) solution of the nonstandard initial value problem y′=f(t,y,y′), y(t0)=y0 under certain natural hypotheses on f. In this paper,
we studied the stability of solutions of a nonstandard first order ordinary
differential system.