Solution-tube and existence results for fourth-order differential equations system

Bouharket Bendouma; Fatima Zohra Ladrani; Keltoum Bouhali; Ahmed Hammoudi; Loay Alkhalifa; Bouharket Bendouma; Fatima Zohra Ladrani; Keltoum Bouhali; Ahmed Hammoudi; Loay Alkhalifa

doi:10.3934/math.20241571

AIMS Mathematics

2024, Volume 9, Issue 11: 32831-32848. doi: 10.3934/math.20241571

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Research article

Solution-tube and existence results for fourth-order differential equations system

1.
Faculty of Mathematics and Informatics, Ibn Khaldoun, University of Tiaret, Algeria
2.
Department of Exact Sciences, Higher Training Teacher's School of Oran Ammour Ahmed (ENSO), Oran, Algeria
3.
Department of Mathematics, College of Science, Qassim University, Saudi Arabia
4.
Laboratory of Mathematics, Ain Témouchent University P.O. Box 89, 46000 Ain Témouchent, Algeria

Received: 07 September 2024 Revised: 04 November 2024 Accepted: 12 November 2024 Published: 20 November 2024
MSC : 34A34, 34A60, 34B15, 47H10

In the present paper, we examine the existence of solutions to fourth-order differential equation systems when the $ L^{1} $-Carathéodory function is on the right-hand side. A concept of solution-tube for these issues is presented. The concepts of upper and lower solutions for fourth-order differential equations are extended to systems owing to this idea.
- fourth-order systems of differential equations,
- iterative methods,
- solution-tubes,
- existence theorems,
- Leray-Schauder degree
Citation: Bouharket Bendouma, Fatima Zohra Ladrani, Keltoum Bouhali, Ahmed Hammoudi, Loay Alkhalifa. Solution-tube and existence results for fourth-order differential equations system[J]. AIMS Mathematics, 2024, 9(11): 32831-32848. doi: 10.3934/math.20241571

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Abstract

In the present paper, we examine the existence of solutions to fourth-order differential equation systems when the $ L^{1} $-Carathéodory function is on the right-hand side. A concept of solution-tube for these issues is presented. The concepts of upper and lower solutions for fourth-order differential equations are extended to systems owing to this idea.

References

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