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Research Article | Open Access

Existence theory for a third-order ordinary differential equation with non-separated multi-point and nonlocal Stieltjes boundary conditions

Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah 23218, Saudi Arabia
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Abstract

This study develops the existence of solutions for a nonlinear third-order ordinary differential equation with non-separated multi-point and nonlocal Riemann-Stieltjes boundary conditions. Standard tools of fixed point theorems are applied to prove the existence and uniqueness of results for the problem at hand. Further, we made use of the fixed point theorem due to Bohnenblust-Karlin to discuss the existence of solutions for the multi-valued case. Lastly, we clarify the reported results by means of examples.

Keywords

Stieltjes boundary conditionsnonlocalmulti-pointexistenceuniquenessfixed pointBohnenblust-Karlin
CLC number: 34A60, 34B10, 34B15

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AIMS Mathematics
Volume 8 Issue 6,
June 2023
Pages 13572-13592
DOI: 10.3934/math.2023689

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Cite this article:
Alsulami M. Existence theory for a third-order ordinary differential equation with non-separated multi-point and nonlocal Stieltjes boundary conditions. AIMS Mathematics, 2023, 8(6): 13572-13592. https://doi.org/10.3934/math.2023689

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Received: 10 January 2023
Revised: 07 March 2023
Accepted: 13 March 2023
Published: 15 June 2023
©2023 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)