Abstract
with odd f~ C(R). In contrast to the one-dimensional ordinary differential equation this equation can have periodic solutions as the example i(t) = -7r/2 x(t 1) with solutions x(t) = z sin(rc/2 t), z > 0 shows. Numerical bifurcation diagrams (e.g., [6, 143) indicate a complicated structure of the period solutions depending on the delay parameter u.. One finds various intersecting smooth curves. One task of mathematics is to prove the existence of periodic solutions. In this paper we are mainly interested in symmetric periodic solutions, i.e., solutions x of (c$) which fultil the symmetry property
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