Journal of Applied Mathematics and Stochastic Analysis
Volume 4 (1991), Issue 3, Pages 211-224

Stability of solutions of a nonstandard ordinary differential system by Lyapunov's second method

M. Venkatesulu and P. D. N. Srinivasu

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.


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.