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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.

MSC:
39A20 Multiplicative and other generalized difference equations, e.g., of Lyness type
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