Abstract
The object of this paper is to study the stability and asymptotic stability of solutions of the non-linear differential equation dx dt = A(t)x + f(t,x) by using the method of equivalent inner products. This method enables one to determine a stability region without the ingenuity in constructing a Lyapunov function. It shows also that for an unstable linear system it is possible to choose a non-linear function so that the non-linear system is stable or asymptotically stable. Both global and regional stability are discussed.
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