Convergence Results on a Second-Order Rational Difference Equation with Quadratic Terms
<p/> <p>We investigate the global behavior of the second-order difference equation <inline-formula><graphic file="1687-1847-2009-985161-i1.gif"/></inline-formula>, where initial conditions and all coefficients are positive. We find conditions on <inline-for...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2009-01-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://www.advancesindifferenceequations.com/content/2009/985161 |
| Summary: | <p/> <p>We investigate the global behavior of the second-order difference equation <inline-formula><graphic file="1687-1847-2009-985161-i1.gif"/></inline-formula>, where initial conditions and all coefficients are positive. We find conditions on <inline-formula><graphic file="1687-1847-2009-985161-i2.gif"/></inline-formula> under which the even and odd subsequences of a positive solution converge, one to zero and the other to a nonnegative number; as well as conditions where one of the subsequences diverges to infinity and the other either converges to a positive number or diverges to infinity. We also find initial conditions where the solution monotonically converges to zero and where it diverges to infinity.</p> |
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| ISSN: | 1687-1839 1687-1847 |