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RATIONAL DIFFERENCE EQUATIONS WITH POSITIVE EQUILIBRIUM POINT
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 Title & Authors
RATIONAL DIFFERENCE EQUATIONS WITH POSITIVE EQUILIBRIUM POINT
Dubickas, Arturas;
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 Abstract
In this note we study positive solutions of the mth order rational difference equation , where n = m,m+1,m+2, and > 0. We describe a sufficient condition on nonnegative real numbers under which every solution of the above equation tends to the limit /2B as , where and .
 Keywords
difference equations;equilibrium point;convergence of sequences;upper and lower limits;
 Language
English
 Cited by
1.
On the Difference equation xn+1=axn−l+bxn−k+cxn−sdxn−s−e, Mathematical Methods in the Applied Sciences, 2017, 40, 3, 535  crossref(new windwow)
 References
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E. Camouzis, Global analysis of solutions of ${x_{n+1}}=\frac{{\beta}x_n+{\delta}x_{n-2}}{A+Bx_{n}+Cx_{n-1}}$, J. Math. Anal. Appl. 316 (2006), no. 2, 616-627. crossref(new window)

2.
E. Camouzis and G. Ladas, Dynamics of Third-Order Rational Difference Equations with Open Problems and Conjectures, Advances in Discrete Mathematics and Applications, 5. Chapman & Hall/CRC, Boca Raton, FL, 2008.

3.
M. R. S. Kulenovic and G. Ladas, Dynamics of Second Order Rational Difference Equations, With open problems and conjectures. Chapman & Hall/CRC, Boca Raton, FL, 2002.

4.
J. Park, A global behavior of the positive solutions of ${x_{n+1}}=\frac{{\beta}x_n+x_{n-2}}{A+Bx_{n}+x_{n-2}}$, Commun. Korean Math. Soc. 23 (2008), no. 1, 61-65. crossref(new window)