Progress report on the boundedness character of third-order rational equations

Camouzis, E.; Chatterjee, Esha; Ladas, G.; Quinn, E. P.

doi:10.1080/10236190500272897

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Difference Inequalities Comparison Tests and Some Conseque1

Introduction1

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2006

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Cited by 14 publications

(2 citation statements)

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“…These boundedness results were completely established in [Camouzis et al 2006]. For related works, see [Kocić and Ladas 1993;Kulenović and Ladas 2002;Camouzis et al 2004a;2004b;2005a;2005b;2006;Grove and Ladas 2005;Camouzis 2006].…”

Section: Difference Inequalities Comparison Tests and Some Consequementioning

confidence: 85%

Difference inequalities, comparison tests, and some consequences

Palladino

2008

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Difference inequalities, comparison tests, and some consequences We study the behavior of nonnegative sequences which satisfy certain difference inequalities. Several comparison tests involving difference inequalities are developed for nonnegative sequences. Using the aforementioned comparison tests, it is possible to determine the global stability and boundedness character for nonnegative solutions of particular rational difference equations in a range of their parameters.

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Section: Difference Inequalities Comparison Tests and Some Consequementioning

confidence: 85%

Difference inequalities, comparison tests, and some consequences

Palladino

2008

Involve

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“…See also [1] where we established the boundedness of solutions of a similar equation, namely #832. For some related work see [1][2][3][4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

On the dynamics of xn+1=δxn−2+xn−3
Camouzis
¹
,
Chatterjee
²
,
Ladas
³

2007
Journal of Mathematical Analysis and Applications
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We investigate the global character of solutions of the equation in the title with positive parameters and with arbitrary nonnegative initial conditions. In particular we show that every solution of the equation is bounded. We find necessary and sufficient conditions for the global asymptotic stability of the zero equilibrium. We also investigate the positive equilibrium and find regions of parameters where the positive equilibrium is a global attractor of all positive solutions.

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