Global behavior of the max-type difference equation \(x_{n}=\max \{\frac{A_1}{x^{\alpha_1}_{n-m\_1}}, \frac{a_2}{x^{\alpha_2}\_{n-m_2}},\dots,\frac{A_k}{x^{\alpha_k}\_{n-m_k}} \}\)
The authors show that any positive solution of the difference equation NEWLINE\[NEWLINE x_{n}=\max\left\{\frac{A_1}{x^{\alpha_1}_{n-m_1}},\frac{A_2}{x^{\alpha_2}_{n-m_2}},\dots,\frac{A_k}{x^{\alpha_k}_{n-m_k}}\right\}, \;\;n=0,1,\dots, NEWLINE\]NEWLINE where \(A_i>0\), \(\alpha_i\in(0,1)\), \(m_i\) is a natural number for \(i=1,\dots,k\), \(A_i^{\frac{1}{1+\alpha_i}}\leq A_{i+1}^{\frac{1}{1+\alpha_{i+1}}}\) for \(i=1,\dots,k-1\), converges to \(A_k^{\frac{1}{1+\alpha_k}}\).
scientific article; zbMATH DE number 6058728