Journal of Applied Mathematics and Stochastic Analysis
Volume 5 (1992), Issue 3, Pages 261-274
Boundedness and asymptotic stability in the large of solutions of an ordinary differential system
Department of Mathematics, Sri Sathya Sai Institute of Higher Learning, Prasanthinilayam 515 134, Andhra Pradesh, India
Received 1 February 1991; Revised 1 December 1991
Copyright © 1992 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 , where is not
necessarily linear in its arguments, represent certain physical phenomena
and solutions have been known for quite some time. The well known
Clairut's and Chrystal's equations fall into this category. Earlier
existence of solutions of first order initial value problems and stability of
solutions of first order ordinary differential system of the above type were
established. In this paper we study boundedness and asymptotic stability
in the large of solutions of an ordinary differential system of the above
type under certain natural hypotheses on .