Document Zbl 1481.39012

Existence of the asymptotically periodic solution to the system of nonlinear neutral difference equations. (English) Zbl 1481.39012

Tatra Mt. Math. Publ. 79, 149-162 (2021).

Summary: The system of nonlinear neutral difference equations with delays in the form \[ \begin{cases} \Delta \bigl(y_i(n) + p_i(n)y_i(n - \tau_i)\bigr) = a_i(n)f_i(y_{i+1}(n)) + g_i(n),\\ \Delta \bigl(y_m(n) + p_m(n)y_m(n - \tau_m)\bigr) = a_m(n)f_m(y_1(n)) + g_m(n), \end{cases} \] for \(i = 1,\dots, m - 1, m \geq 2\), is studied. The sufficient conditions for the existence of an asymptotically periodic solution of the above system, are established. Here sequences \((p_i(n)), i = 1,\dots, m\), are bounded away from \(-1\). The presented results are illustrated by theoretical and numerical examples.

Cited in 1 Document

MSC:

39A23	Periodic solutions of difference equations
39A22	Growth, boundedness, comparison of solutions to difference equations

Keywords:

difference equation; delays; neutral type; periodicity; asymptotic behaviour

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