Bounds for solutions of perturbed differential equations

Abstract:

A modified form of the Alekseev variation of constants equation is used to relate the solutions of systems of the form $\dot x = f(t,x,\lambda ),\lambda$ in ${R^m}$ and the perturbed system $\dot y = f(t,y,\psi (t)) + g(t,y)$. Hypotheses are given on the $m$ parameter family of differential equations $\dot x = f(t,x,\lambda )$ so that if $\dot \psi$ and $g$ are perturbation functions, bounds can be calculated for the solutions of the perturbed system.