Abstract
By a system of periodic differential equations referred to in the title we mean a system of the form f(t, U, u’) = 0, where u = u(t), u’ = du/dt, and f(t, u, v) = f(t + r, u, w). Our particular approach will be to break up the vector u into two vector components so that our system becomes f(t, X, y, x’, y’) = 0, where x is an m-dimensional vector, y is n-dimensional, and f is m + n dimensional. Either m or n may be zero, in which case the system is independent of x or y respectively. We shall impose conditions only on x which, however, will yield properties valid for y as well. Throughout the paper, we shall assume that there exists a unique solution through any prescribed point in a region in (t, X, y) space, and that the variables always remain in this region. These requirements will not be explicitly stated. In the first part of the paper we shall discuss systems of arbitrary order. In the second part, these results will be specialized to second order scalar differential equations.
Published Version
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