A stability theory for perturbed differential equations

Abstract

The problem of determining the behavior of the solutions of a perturbed differential equation with respect to the solutions of the original unperturbed differential equation is studied. The general differential equation considered is X′=f(t,X) and the associated perturbed differential equation is Y′=f(t,Y)+g(t,Y).

Keywords

• Liapunov functions
• asymptotic behavior of solutions
• asymptotic equivalence.