On the existence of unbounded solutions for some rational equations

We show that whenever parameters are nonnegative, $A < δ$ , and $C, E > 0$ , unbounded solutions exist for some choice of nonnegative initial conditions. We also partly resolve a conjecture regarding the boundedness character of the rational difference equation

x_{n} = \frac{x_{n - 3}}{B x_{n - 1} + x_{n - 4}}, n \in ℕ .

We show that whenever $B > 2^{5}$ , unbounded solutions exist for some choice of nonnegative initial conditions.

Keywords

difference equation, periodic convergence, boundedness character, unbounded solutions, periodic behavior of solutions of rational difference equations, nonlinear difference equations of order greater than one, global asymptotic stability

Mathematical Subject Classification 2000

Primary: 39A10, 39A11

Milestones

Received: 8 December 2008

Accepted: 9 December 2008

Published: 7 May 2009

Communicated by Kenneth S. Berenhaut

Authors

Gabriel Lugo
Department of Mathematics University of Rhode Island 5 Lippitt Road Kingston, RI 02881 United States

Vol. 2, No. 2, 2009

Gabriel Lugo

Abstract

Keywords

Mathematical Subject Classification 2000

Milestones

Authors