A Novel Study on the Non-Negative Solution of an Eighth-Order BVP

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DOI: https://doi.org/10.28924/2291-8639-23-2025-256
Published: Oct 16, 2025
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Zouaoui Bekri, Vedat Suat Erturk, Mohammad Esmael Samei, Dania Santina, Nabil Mlaiki, A Novel Study on the Non-Negative Solution of an Eighth-Order BVP, Int. J. Anal. Appl., 23 (2025), 256.

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Zouaoui Bekri, Vedat Suat Erturk, Mohammad Esmael Samei, Dania Santina, Nabil Mlaiki

Abstract

In this article, we investigate the existence of non-negative solutions for a boundary value problem associated with an eighth-order differential equation \(\lambda^{(8)} ( \varpi)  = \psi( \varpi, \lambda(\varpi)\), \(\lambda^{(1)}( \varpi), \cdots, \lambda^{(7)} (\varpi))\) for \(0 < \varpi < 1\), under initial values \(\lambda(0)=\lambda^{'}(0) = \lambda^{''}(0) = \lambda^{'''}(0) =0\) and \(\lambda^{(4)}(1) = \lambda^{(5)}(1) = \lambda^{(6)}(1) = \lambda^{(7)}(1) = 0\), where \(\psi\) is  non-negative continuous function. For this study, we use the nonlinear Leray-Schauder alternative and the Leray-Schauder fixed-point theorem to prove the existence of at least one non-negative solution. As a numerical application, we present an example to confirm the utility of the achieved results.

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