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2009 On the existence of unbounded solutions for some rational equations
Gabriel Lugo
Involve 2(2): 237-247 (2009). DOI: 10.2140/involve.2009.2.237

Abstract

We resolve several conjectures regarding the boundedness character of the rational difference equation

x n = α + δ x n 3 A + B x n 1 + C x n 2 + E x n 4 , n .

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 = x n 3 B x n 1 + x n 4 , n .

We show that whenever B>25, unbounded solutions exist for some choice of nonnegative initial conditions.

Citation

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Gabriel Lugo. "On the existence of unbounded solutions for some rational equations." Involve 2 (2) 237 - 247, 2009. https://doi.org/10.2140/involve.2009.2.237

Information

Received: 8 December 2008; Accepted: 9 December 2008; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1189.39015
MathSciNet: MR2501340
Digital Object Identifier: 10.2140/involve.2009.2.237

Subjects:
Primary: 39A10, 39A11

Rights: Copyright © 2009 Mathematical Sciences Publishers

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