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Existence of bounded positive solutions for a system of difference equations. (English) Zbl 1245.39013

The authors study the system \[ \begin{aligned} \Delta[a_n \Delta(x_n+ b_nx_{n-\tau})] &+ f(n, x_{h_{1n}},\dots, x_{h_{kn}}, y_{w_{1n}},\dots, y_{w_{kn}})= c_n,\\ \Delta[p_n \Delta(y_n+ q_ny_{n-\sigma})] &+ g(n, x_{s_{1n}},\dots, s_{s_{kn}}, y_{t_{1n}},\dots, y_{t_{kn}})= r_n\end{aligned} \] under conditions which guarantee the existence of uncountable bounded positive solutions.

MSC:

39A22 Growth, boundedness, comparison of solutions to difference equations
39A10 Additive difference equations
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