A note on unbounded solutions of a class of second order rational difference equations

2006 ◽  
Vol 12 (7) ◽  
pp. 777-781 ◽  
Author(s):  
M. R. S. Kulenović ◽  
O. Merino
Keyword(s):  
Difference Equations ◽  
Second Order ◽  
Unbounded Solutions ◽  
Rational Difference Equations

Unboundedness results for systems

2009 ◽  
Vol 7 (4) ◽  
Author(s):  
Gabriel Lugo ◽  
Frank Palladino
Keyword(s):  
Difference Equations ◽  
Initial Conditions ◽  
Unbounded Solutions ◽  
Rational Difference Equations

AbstractWe 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.

scholarly journals On the Solutions of Four Second-Order Nonlinear Difference Equations

2019 ◽  
Author(s):  
İnci Okumuş ◽  
Yüksel Soykan
Keyword(s):  
Difference Equations ◽  
Second Order ◽  
Global Behavior ◽  
Nonlinear Difference Equations ◽  
Rational Difference Equations ◽  
The Stability

This paper deals with the form, the stability character, the periodicity and the global behavior of solutions of the following four rational difference equations x_{n+1} = ((±1)/(x_{n}(x_{n-1}±1)-1)) x_{n+1} = ((±1)/(x_{n}(x_{n-1}∓1)+1)).

scholarly journals On monotone solutions of some classes of difference equations

2006 ◽  
Vol 2006 ◽  
pp. 1-9 ◽  
Author(s):  
Stevo Stevic
Keyword(s):  
Difference Equations ◽  
Present Author ◽  
Second Order ◽  
Open Problems ◽  
Rational Difference Equations ◽  
Monotone Solutions

We describe a method for finding monotone solutions of some classes of difference equations converging to the corresponding equilibria. The method enables us to confirm three conjectures posed by the present author in a talk, which are extensions of three conjectures by M. R. S. Kulenović and G. Ladas,Dynamics of Second Order Rational Difference Equations. With Open Problems and Conjectures. Chapman and Hall/CRC, 2002. It is interesting that the method, in some cases, can be applied also when the parameters are variable.

scholarly journals Oscillatory behavior of second order unstable type neutral difference equations

2005 ◽  
Vol 36 (1) ◽  
pp. 57-68
Author(s):  
E. Thandapani ◽  
S. Pandian ◽  
R. K. Balasubramanian
Keyword(s):  
Positive Integer ◽  
Difference Equation ◽  
Difference Equations ◽  
Neutral Type ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Neutral Difference Equations ◽  
Unbounded Solutions ◽  
Unstable Type ◽  
Positive Integers

This paper deals with the oscillatory behavior of all bounded/ unbounded solutions of second order neutral type difference equation of the form$$ \Delta (a_n(\Delta_c y_n+py_{n-k}))^\alpha)-g_nf(y_{\sigma(n)})=0, $$where $ p $ is real, $ \alpha $ is a ratio of odd positive integers, $ k $ is a positive integer and $ \{\sigma(n)\} $ is a sequence of integers. Examples are provided to illustrate the results.

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