Properties of a Certain Lyness Equation

✍ Scribed by C. Darwen; W.T. Patula

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 231 KB
• Volume: 218
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.1997.5812

✦ Synopsis

We investigate oscillation, cycle length, and extreme values for the difference equation x n+1 = a + k-1 i=0 b i x n-i /x n-k , where a and b i are nonnegative numbers and a + k-1 i=0 b i > 0. If a > 0, it is known from Theorem 2.2.1 of V. L. Kocic, G. Ladas, and I. W. Rodrigues (J. Math. Anal. Appl. 173, 1993, 127-157) that every cycle has no more than 2k + 1 terms. If a = 0, we show this is not necessarily true. A general statement concerning cycle length if a = 0 remains an open question.