Some boundedness results for systems of two rational difference equations

• Autorzy: Gabriel Lugo , Frank Palladino
• Języki publikacji: EN

Abstrakty

EN

We study k th order systems of two rational difference equations $$ x_n = \frac{{\alpha + \sum\nolimits_{i = 1}^k {\beta _i x_{n - 1} + } \sum\nolimits_{i = 1}^k {\gamma _i y_{n - 1} } }} {{A + \sum\nolimits_{j = 1}^k {B_j x_{n - j} + } \sum\nolimits_{j = 1}^k {C_j y_{n - j} } }}, y_n = \frac{{p + \sum\nolimits_{i = 1}^k {\delta _i x_{n - i} + } \sum\nolimits_{i = 1}^k {\varepsilon _i y_{n - i} } }} {{q + \sum\nolimits_{j = 1}^k {D_j x_{n - j} + } \sum\nolimits_{j = 1}^k {E_j y_{n - j} } }} n \in \mathbb{N} $$. In particular, we assume non-negative parameters and non-negative initial conditions, such that the denominators are nonzero. We develop several approaches which allow us to extend well known boundedness results on the k th order rational difference equation to the setting of systems in certain cases.

Słowa kluczowe

EN

Difference equation; Systems; Boundedness character

Kategorie tematyczne

• 39A10: Difference equations, additive

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 6
• Strony: 1058-1090

Daty

wydano

2010-12-01

online

2010-10-30

Twórcy

autor

Gabriel Lugo

• University of Rhode Island

autor

Frank Palladino

• University of Rhode Island

Bibliografia

• [1] Camouzis E., Kulenovic M.R.S., Ladas G., Merino O., Rational systems in the plane, J. Difference Equ. Appl., 2009, 15(3), 303–323 http://dx.doi.org/10.1080/10236190802125264
• [2] Camouzis E., Ladas G., Global results on rational systems in the plane, part 1, J. Difference Equ. Appl., 2010, 16(8), 975–1013 http://dx.doi.org/10.1080/10236190802649727
• [3] Camouzis E., Ladas G., Palladino F., Quinn E.P., On the boundedness character of rational equations, part 1, J. Difference Equ. Appl., 2006, 12(5), 503–523 http://dx.doi.org/10.1080/10236190500539311
• [4] Knopf P.M., Huang Y.S., On the boundedness character of some rational difference equations, J. Difference Equ. Appl., 2008, 14(7), 769–777 http://dx.doi.org/10.1080/10236190701852695
• [5] Lugo G., Palladino F.J., Unboundedness results for systems, Cent. Eur. J. Math., 2009, 7(4), 741–756 http://dx.doi.org/10.2478/s11533-009-0051-2
• [6] Palladino F.J., Difference inequalities, comparison tests, and some consequences, Involve, 2008, 1(1), 91–100

Identyfikatory

DOI

10.2478/s11533-010-0063-y