Abstract
SynopsisSchaefer's fixed-point theorem is used to obtain sufficient conditions for the existence of a periodic solution of the non-linear differential equation f(D)x+BMg(D)x = p. The most significant feature of these conditions is a geometrical restriction on the range of the matrix M which is the same as the elliptic ball criterion encountered in stability theory. The extension of the results to delay-differential equations with constant time lags is also discussed.
Publisher
Cambridge University Press (CUP)
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1. The Poincaré–Bendixson theorem for certain differential equations of higher order;Proceedings of the Royal Society of Edinburgh: Section A Mathematics;1979
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