Boundedness and Asymptotic Stability in the Large of Solutions of an Ordinary Differential System y′ = f{t,y,y′)

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 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 f. © 1993, The Society of Applied Mathematics, Modeling and Simulation.