Unboundedness results for systems

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

Abstrakty

EN

We study k th order systems of two rational difference equations $$ x_n = \frac{{\alpha + \sum\nolimits_{i = 1}^k {\beta _i x_{n - i} + } \sum\nolimits_{i = 1}^k {\gamma _i y_{n - i} } }} {{A + \sum\nolimits_{j = 1}^k {B_j x_{n - j} + } \sum\nolimits_{j = 1}^k {C_j y_{n - j} } }},n \in \mathbb{N}, $$ 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.

Słowa kluczowe

EN

Difference equation; Systems; Unbounded solutions

Kategorie tematyczne

• 39A10: Difference equations, additive

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2009
• Tom: 7
• Numer: 4
• Strony: 741-756

Daty

wydano

2009-12-01

online

2009-10-31

Twórcy

autor

Gabriel Lugo

• Department of Mathematics, University of Rhode Island, Kingston, USA

autor

Frank Palladino

• Department of Mathematics, University of Rhode Island, Kingston, USA

Bibliografia

• [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]
• [2] Camouzis E., Ladas G., Global results on rational systems in the plane, Part 1, J. Difference Equa. Appl., to appear
• [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]
• [4] Palladino F.J., Difference inequalities, comparison tests, and some consequences, Involve, 2008, 1, 91–100
• [5] Palladino F.J., On periodic trichotomies, J. Difference Equa. Appl., 2009, 15, 605–620 http://dx.doi.org/10.1080/10236190802258677[Crossref]

Identyfikatory

DOI

10.2478/s11533-009-0051-2