Existence of nonperiodic solutions of the Lyness equation x(n+1)=(alpha+x(n))/x(n-1)

[摘要] G. Ladas (J. Difference Equations Appl., 1995) proposed the following conjecture: Assume that alpha is an element of (0, 1) boolean OR (1, infinity). Show that the equation x(n + 1) = alpha + x(n)/x(n - 1), n = 0, 1,... has positive solutions which are not periodic. The truth of the conjecture is verified in this paper. (C) 1997 Academic Press.

[发布日期] 1997-05-01