Several perturbation theorems are proved for nonlinear ordinary differential systems x′ = f(t, x) for which the zero solution is uniformly stable in variation. This type of stability is, in general, more restrictive than uniform stability but is equivalent to it in the linear case. Under various growth conditions on g(t, x), the behavior of solutions of x′ = f(t, x) + g(t, x) is studied.
ASJC Scopus subject areas
- Applied Mathematics