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**On a max-type difference equation.**
*(English)*
Zbl 1152.39016

The authors study the solutions of

\[ x_{n+1} = \max\left\{{{1}\over{x_n}},Ax_{n-1}\right\},\quad n\in N_0,\quad A\in \mathbb R; \]

the initial conditions \(x_{-1}\) and \(x_0\) are non-zero real numbers. The cases \(A<0\) and \(A>0\) are discussed separately. Each case has several sub-cases according to the possible sign combinations for the initial conditions. Additional conditions on \(A\) are considered.

\[ x_{n+1} = \max\left\{{{1}\over{x_n}},Ax_{n-1}\right\},\quad n\in N_0,\quad A\in \mathbb R; \]

the initial conditions \(x_{-1}\) and \(x_0\) are non-zero real numbers. The cases \(A<0\) and \(A>0\) are discussed separately. Each case has several sub-cases according to the possible sign combinations for the initial conditions. Additional conditions on \(A\) are considered.

Reviewer: Vladimir Răsvan (Craiova)

### MSC:

39A20 | Multiplicative and other generalized difference equations |

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\textit{I. Yalçinkaya} et al., Discrete Dyn. Nat. Soc. 2007, Article ID 47264, 10 p. (2007; Zbl 1152.39016)

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### References:

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