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It is shown that cyclic di¤erential systems of the forms (A) x 0 i 1⁄4 piðtÞx ai iþ1, i 1⁄4 1; . . . ; n ðxnþ1 1⁄4 x1Þ, and (B) x 0 i 1⁄4 piðtÞx ai iþ1 , i 1⁄4 1; . . . ; n ðxnþ1 1⁄4 x1Þ, where ai > 0, i 1⁄4 1; . . . ; n, are constants and piðtÞ > 0, i 1⁄4 1; . . . ; n, are continuous functions on 1⁄20;yÞ may possess singular solutions of extinct type, that is, those positive solutions ðx1ðtÞ; . . . ; xnðtÞÞ of (A) (resp. (B)) which are defined on some finite interval 1⁄2t0;TÞ, 0a t0 < T < y, and satisfy xiðtÞ > 0, t A 1⁄2t0;TÞ, and limt!T 0 xiðtÞ 1⁄4 0, i 1⁄4 1; . . . ; n.

Extinct Singular Solutions of First Order Systems of Nonlinear Differential Equations