Geodesic
Oscillation criteria for two dimensional linear neutral delay difference systems
Mathematica Bohemica, Tome 148 (2023) no. 4, pp. 447-460

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In this work, necessary and sufficient conditions for the oscillation of solutions of 2-dimensional linear neutral delay difference systems of the form $$ \Delta \left [\begin{matrix} x(n)+p(n)x(n-m)\\ y(n)+p(n)y(n-m) \end{matrix} \right ]= \left [\begin{matrix} a(n) b(n) \\ c(n) d(n) \end{matrix} \right ]\left [\begin{matrix} x(n-\alpha )\\ y(n-\beta ) \end{matrix} \right ] $$ are established, where $m>0$, $\alpha \geq 0$, $\beta \geq 0$ are integers and $a(n)$, $b(n)$, $c(n)$, $d(n)$, $p(n)$ are sequences of real numbers.
DOI : 10.21136/MB.2022.0048-21
Classification : 34C10, 34K11, 39A13
Keywords: oscillation; nonoscillation; system of neutral equations; Krasnoselskii's fixed point theorem 
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Tripathy, Arun Kumar. Oscillation criteria for two dimensional linear neutral delay difference systems. Mathematica Bohemica, Tome 148 (2023) no. 4, pp. 447-460. doi: 10.21136/MB.2022.0048-21

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