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

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Journal of Applied Mathematics and Stochastic Analysis
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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.

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