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Research Article | Open Access

Existence and nonexistence outcomes for a third-order q-difference equation

Department of Mathematics, Istanbul Beykent University, İstanbul 34500, Türkiye; Email: nihanturan@beykent.edu.tr
Department of Mathematics, Faculty of Sciences, Sakarya University, Sakarya 54050, Türkiye
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Abstract

In this paper, using the Schauder and the Banach fixed point (FP) theorems, we examine the existence and uniqueness of solutions in the Banach space C ( [ 0 , 1 ] ) for a boundary value problem (BVP) of non-linear third-order q-difference equations with the q-integral boundary condition. Then, we impose the sufficient condition that allows us to deduce a nonexistence result. Furthermore, we offer some examples to support our main outcomes.

Keywords

boundary value problemsq-difference equationsintegral-type boundary conditionsGreen's functionfixed point theorems
CLC number: 39A13, 47H10

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AIMS Mathematics
Volume 10 Issue 11,
November 2025
Pages 27044-27057
DOI: 10.3934/math.20251188

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Cite this article:
Turan N, Şahin A. Existence and nonexistence outcomes for a third-order q-difference equation. AIMS Mathematics, 2025, 10(11): 27044-27057. https://doi.org/10.3934/math.20251188

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Received: 10 September 2025
Revised: 03 November 2025
Accepted: 17 November 2025
Published: 21 November 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)