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Periodic solutions for $dot x=Ax+g(x,,t)+varepsilon p(t)$

1971
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Canadian mathematical bulletin
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We wish to establish the existence of a periodic solution to (1) x = Ax+g(x, t) + ep(t), ( # = d/dt) where x, g and p are «-vectors, A is an n x n constant matrix, and € is a small scalar parameter. We assume that g and p are locally Lipschitz in x and continuous and T-periodic in t, and that the origin is a point of asymptotically stable equilibrium, when € = 0. Although the result below is not new ([1], [2]), the proof is simple and of some interest and provides an explicit bound on c which

doi:10.4153/cmb-1971-105-4
fatcat:ep3sac2utjbenpilsvnnwvhv3y