Unboundedness results for systems

Gabriel Lugo; Frank Palladino

Open Mathematics (2009)

  • Volume: 7, Issue: 4, page 741-756
  • ISSN: 2391-5455

Abstract

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We study k th order systems of two rational difference equations x n = α + ∑ i = 1 k β i x n - i + ∑ i = 1 k γ i y n - i A + ∑ j = 1 k B j x n - j + ∑ j = 1 k C j y n - j , n ∈ ℕ , In particular we assume non-negative parameters and non-negative initial conditions. We develop several approaches which allow us to prove that unbounded solutions exist for certain initial conditions in a range of the parameters.

How to cite

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Gabriel Lugo, and Frank Palladino. "Unboundedness results for systems." Open Mathematics 7.4 (2009): 741-756. <http://eudml.org/doc/269268>.

@article{GabrielLugo2009,
abstract = {We study k th order systems of two rational difference equations \[ x\_n = \frac\{\{\alpha + \sum \nolimits \_\{i = 1\}^k \{\beta \_i x\_\{n - i\} + \} \sum \nolimits \_\{i = 1\}^k \{\gamma \_i y\_\{n - i\} \} \}\}\{\{A + \sum \nolimits \_\{j = 1\}^k \{B\_j x\_\{n - j\} + \} \sum \nolimits \_\{j = 1\}^k \{C\_j y\_\{n - j\} \} \}\},n \in \mathbb \{N\}, \] In particular we assume non-negative parameters and non-negative initial conditions. We develop several approaches which allow us to prove that unbounded solutions exist for certain initial conditions in a range of the parameters.},
author = {Gabriel Lugo, Frank Palladino},
journal = {Open Mathematics},
keywords = {Difference equation; Systems; Unbounded solutions; systems of difference equations; unbounded solutions},
language = {eng},
number = {4},
pages = {741-756},
title = {Unboundedness results for systems},
url = {http://eudml.org/doc/269268},
volume = {7},
year = {2009},
}

TY - JOUR
AU - Gabriel Lugo
AU - Frank Palladino
TI - Unboundedness results for systems
JO - Open Mathematics
PY - 2009
VL - 7
IS - 4
SP - 741
EP - 756
AB - We study k th order systems of two rational difference equations \[ x_n = \frac{{\alpha + \sum \nolimits _{i = 1}^k {\beta _i x_{n - i} + } \sum \nolimits _{i = 1}^k {\gamma _i y_{n - i} } }}{{A + \sum \nolimits _{j = 1}^k {B_j x_{n - j} + } \sum \nolimits _{j = 1}^k {C_j y_{n - j} } }},n \in \mathbb {N}, \] In particular we assume non-negative parameters and non-negative initial conditions. We develop several approaches which allow us to prove that unbounded solutions exist for certain initial conditions in a range of the parameters.
LA - eng
KW - Difference equation; Systems; Unbounded solutions; systems of difference equations; unbounded solutions
UR - http://eudml.org/doc/269268
ER -

References

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  1. [1] Camouzis E., Kulenović M.R.S., Ladas G., Merino O., Rational systems in the plane, J. Difference Equa. Appl., 2009, 15, 303–323 http://dx.doi.org/10.1080/10236190802125264[Crossref] Zbl1169.39010
  2. [2] Camouzis E., Ladas G., Global results on rational systems in the plane, Part 1, J. Difference Equa. Appl., to appear Zbl1218.39001
  3. [3] Camouzis E., Ladas G., Palladino F., Quinn E.P., On the boundedness character of rational equations, Part 1, J. Difference Equa. Appl., 2006, 12, 503–523 http://dx.doi.org/10.1080/10236190500539311[Crossref][WoS] Zbl1104.39003
  4. [4] Palladino F.J., Difference inequalities, comparison tests, and some consequences, Involve, 2008, 1, 91–100 Zbl1154.39012
  5. [5] Palladino F.J., On periodic trichotomies, J. Difference Equa. Appl., 2009, 15, 605–620 http://dx.doi.org/10.1080/10236190802258677[Crossref] Zbl1207.39018

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