Solutions of the Difference Equation 𝑥𝑛+1=𝑥𝑛𝑥𝑛−1−1
Our goal in this paper is to investigate the long-term behavior of solutions of the following difference equation: 𝑥𝑛+1=𝑥𝑛𝑥𝑛−1−1, 𝑛=0,1,2,…, where the initial conditions 𝑥−1 and 𝑥0 are real numbers. We examine the boundedness of solutions, periodicity of solutions, and existence of unbounded solutio...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/469683 |
| Summary: | Our goal in this paper is to investigate the long-term behavior of
solutions of the following difference equation:
𝑥𝑛+1=𝑥𝑛𝑥𝑛−1−1, 𝑛=0,1,2,…,
where the initial conditions 𝑥−1 and 𝑥0 are real numbers. We examine the boundedness of solutions, periodicity of solutions, and
existence of unbounded solutions and how these behaviors depend on initial conditions. |
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| ISSN: | 1085-3375 1687-0409 |