Existence theory for coupled nonlinear third-order ordinary differential equations with nonlocal multi-point anti-periodic type boundary conditions on an arbitrary domain

Bashir Ahmad; Ahmed Alsaedi; Mona Alsulami; Sotiris K. Ntouyas; Bashir Ahmad; Ahmed Alsaedi; Mona Alsulami; Sotiris K. Ntouyas

doi:10.3934/math.2019.6.1634

AIMS Mathematics

2019, Volume 4, Issue 6: 1634-1663. doi: 10.3934/math.2019.6.1634

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Existence theory for coupled nonlinear third-order ordinary differential equations with nonlocal multi-point anti-periodic type boundary conditions on an arbitrary domain

1.
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia
3.
Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece

Received: 27 July 2019 Accepted: 12 September 2019 Published: 14 October 2019
MSC : 34B10, 34B15

In this paper, we derive existence and uniqueness results for a coupled system of nonlinear third order ordinary differential equations equipped with nonlocal multi-point anti-periodic type coupled boundary conditions. Leray-Schauder alternative and Banach contraction mapping principle are the main tools of our study. Examples are constructed for illustrating the obtained results. Under appropriate conditions, our results correspond to the ones for an ant-periodic boundary value problem of nonlinear third order ordinary differential equations.
- system of ordinary differential equations,
- Leray-Schauder,
- Banach,
- existence,
- fixed point
Citation: Bashir Ahmad, Ahmed Alsaedi, Mona Alsulami, Sotiris K. Ntouyas. Existence theory for coupled nonlinear third-order ordinary differential equations with nonlocal multi-point anti-periodic type boundary conditions on an arbitrary domain[J]. AIMS Mathematics, 2019, 4(6): 1634-1663. doi: 10.3934/math.2019.6.1634

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Abstract

In this paper, we derive existence and uniqueness results for a coupled system of nonlinear third order ordinary differential equations equipped with nonlocal multi-point anti-periodic type coupled boundary conditions. Leray-Schauder alternative and Banach contraction mapping principle are the main tools of our study. Examples are constructed for illustrating the obtained results. Under appropriate conditions, our results correspond to the ones for an ant-periodic boundary value problem of nonlinear third order ordinary differential equations.

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