Existence and uniqueness of solutions for the system of first-order nonlinear differential equations with three-point and integral boundary conditions

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Mardanov M. J., Sharifov Y. A., Ismayilova K. E., Zamanova S. A.

EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, vol.12, no.3, pp.756-770, 2019 (ESCI)

• Publication Type: Article / Article
• Volume: 12 Issue: 3
• Publication Date: 2019
• Doi Number: 10.29020/nybg.ejpam.v12i3.3433
• Journal Name: EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS
• Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
• Page Numbers: pp.756-770
• Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

In the paper, the existence and uniqueness of the solutions for the system of the nonlinear first-order ordinary differential equations with three-point and integral boundary conditions are studied. The Green function is constructed and the considered problem is reduced to the equivalent integral equation. The existence and uniqueness of the solutions for the given problem are analyzed by using the Banach contraction principle. The Schaefer's fixed point theorem is then used to prove the existence of the solutions. Finally, the examples are given to verify the given theorems.