Existence of nonoscillatory solution on $ k $-dimensional system of delayed nonlinear discrete equations with $ p $-Laplacian

Urszula Ostaszewska; Ewa Schmeidel; Małgorzata Zdanowicz

doi:10.3934/dcdsb.2024189

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2025. Doi: 10.3934/dcdsb.2024189

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Existence of nonoscillatory solution on $ k $-dimensional system of delayed nonlinear discrete equations with $ p $-Laplacian

University of Bialystok, Poland

^*Corresponding author: Ewa Schmeidel
^*Corresponding author: Ewa Schmeidel

Received: October 2024

Revised: December 2024

Early access: January 2025

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Abstract

The $ k $-dimensional system of delayed discrete nonlinear equations with $ p $-Laplacian in the form

$ \left\{\begin{array}{l} \Delta \phi_{p_i} \left(x_i(n)+q_i(n)\,x_i(n-l_i)-C_i \right) = a_i(n)\,f_i(x_{i+1}(n-m_i))+b_i(n),\\ \Delta \phi_{p_k} \left(x_k(n)+q_k(n)\,x_k(n-l_k) -C_k \right) = a_k(n)\,f_k(x_1(n-m_k))+b_k(n), \end{array}\right. $

where $ i = 1,\dots,k-1 $, $ k\geq 2 $, is considered. This paper aims to present sufficient conditions for the existence of positive bounded persistent solutions of the above system with various $ (q_i(n)) $, $ i = 1,\dots,k $.

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Mathematics Subject Classification: 39A10, 39A22.

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