Abstract
It is shown that cyclic differential systems of the forms (A) x′i = −pi(t)xαii+1, i = 1, ..., n (xn + 1 = x1), and (B) x′i = −pi(t)x−αii+1, i = 1, ..., n (xn+1 = x1), where αi > 0, i = 1, ..., n, are constants and pi(t) > 0, i = 1, ..., n, are continuous functions on [0,∞) may possess singular solutions of extinct type, that is, those positive solutions (x1(t), ..., xn(t)) of (A) (resp. (B)) which are defined on some finite interval [t0,T), 0 ≤ t0 < T < ∞, and satisfy xi(t) > 0, t ∈ [t0, T), and limt→T−0 xi(t) = 0, i = 1, ..., n.
