Existence of Solutions for Fourth-Order Three-Point Boundary Value Problems on the Half-Line via Upper and Lower Solutions

Şerife Müge Ege; Erbil Çetin

doi:10.53570/jnt.1795792

Existence of Solutions for Fourth-Order Three-Point Boundary Value Problems on the Half-Line via Upper and Lower Solutions

Abstract

In this paper, we study on a half-line and demonstrate the existence of unbounded or bounded solutions of the following three-point fourth-order boundary value problem: For all $\xi\in(0,+\infty)$, ${\Phi}''''(\xi)+p(\xi) g(\xi, {\Phi}(\xi), {\Phi}'(\xi), {\Phi}''(\xi),{\Phi}'''(\xi))=0$ with ${\Phi}''(0)= \Lambda$, ${\Phi}(\rho)=B_1$, ${\Phi}'(0)=B_2$, and ${\Phi}'''(+\infty)=\Omega$, where $\rho$ is fixed and $\rho\in(0,+\infty)$, and $g:[0,+\infty)\times \mathbb{R}^4\rightarrow\mathbb{R}$ provides the condition of Nagumo. In order to address this objective, we employ various mathematical techniques, including the upper and lower solution method, Schauder's fixed point theorem, and topological degree theory. By utilizing these methods, we establish sufficient conditions that guarantee the existence of at least one solution, as well as at least three solutions, for the aforesaid problem. To illustrate the significance of the obtained findings, we provide an example demonstrating the practical implications of the results herein.

Keywords

Supporting Institution

Office of Scientific Research Projects Coordination at Ege University

Thanks

This work was supported by the Office of Scientific Research Projects Coordination at Ege University, Grant number: 15-FEN-070.

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Details

Primary Language

English

Subjects

Ordinary Differential Equations, Difference Equations and Dynamical Systems

Journal Section

Research Article

Authors

Şerife Müge Ege
0000-0001-7734-669X
Türkiye

Erbil Çetin ^*
0000-0002-3785-7011
Türkiye

Publication Date

December 31, 2025

Submission Date

October 2, 2025

Acceptance Date

December 17, 2025

Published in Issue

Year 2025 Number: 53

DOI

https://doi.org/10.53570/jnt.1795792

IZ

https://izlik.org/JA44DA36AF

Cite

RIS / Bibtex

APA

Ege, Ş. M., & Çetin, E. (2025). Existence of Solutions for Fourth-Order Three-Point Boundary Value Problems on the Half-Line via Upper and Lower Solutions. Journal of New Theory, 53, 54-76. https://doi.org/10.53570/jnt.1795792

AMA

1.Ege ŞM, Çetin E. Existence of Solutions for Fourth-Order Three-Point Boundary Value Problems on the Half-Line via Upper and Lower Solutions. JNT. 2025;(53):54-76. doi:10.53570/jnt.1795792

Chicago

Ege, Şerife Müge, and Erbil Çetin. 2025. “Existence of Solutions for Fourth-Order Three-Point Boundary Value Problems on the Half-Line via Upper and Lower Solutions”. Journal of New Theory, nos. 53: 54-76. https://doi.org/10.53570/jnt.1795792.

EndNote

Ege ŞM, Çetin E (December 1, 2025) Existence of Solutions for Fourth-Order Three-Point Boundary Value Problems on the Half-Line via Upper and Lower Solutions. Journal of New Theory 53 54–76.

IEEE

[1]Ş. M. Ege and E. Çetin, “Existence of Solutions for Fourth-Order Three-Point Boundary Value Problems on the Half-Line via Upper and Lower Solutions”, JNT, no. 53, pp. 54–76, Dec. 2025, doi: 10.53570/jnt.1795792.

ISNAD

Ege, Şerife Müge - Çetin, Erbil. “Existence of Solutions for Fourth-Order Three-Point Boundary Value Problems on the Half-Line via Upper and Lower Solutions”. Journal of New Theory. 53 (December 1, 2025): 54-76. https://doi.org/10.53570/jnt.1795792.

JAMA

1.Ege ŞM, Çetin E. Existence of Solutions for Fourth-Order Three-Point Boundary Value Problems on the Half-Line via Upper and Lower Solutions. JNT. 2025;:54–76.

MLA

Ege, Şerife Müge, and Erbil Çetin. “Existence of Solutions for Fourth-Order Three-Point Boundary Value Problems on the Half-Line via Upper and Lower Solutions”. Journal of New Theory, no. 53, Dec. 2025, pp. 54-76, doi:10.53570/jnt.1795792.

Vancouver

1.Şerife Müge Ege, Erbil Çetin. Existence of Solutions for Fourth-Order Three-Point Boundary Value Problems on the Half-Line via Upper and Lower Solutions. JNT. 2025 Dec. 1;(53):54-76. doi:10.53570/jnt.1795792