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

Mona Alsulami; Mona Alsulami

doi:10.3934/math.2023689

AIMS Mathematics

2023, Volume 8, Issue 6: 13572-13592. doi: 10.3934/math.2023689

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

Mona Alsulami ^,

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

Received: 10 January 2023 Revised: 07 March 2023 Accepted: 13 March 2023 Published: 07 April 2023
MSC : 34A60, 34B10, 34B15

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.
- Stieltjes boundary conditions,
- nonlocal,
- multi-point,
- existence,
- uniqueness,
- fixed point,
- Bohnenblust-Karlin
Citation: Mona Alsulami. Existence theory for a third-order ordinary differential equation with non-separated multi-point and nonlocal Stieltjes boundary conditions[J]. AIMS Mathematics, 2023, 8(6): 13572-13592. doi: 10.3934/math.2023689

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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.

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