Existence of solution for first-order coupled system with nonlinear coupled boundary conditions.

*(English)*Zbl 1342.34035Summary: The existence of solution for first-order nonlinear coupled system of ordinary differential equations with nonlinear coupled boundary condition (CBC for short) is studied using a coupled lower and upper solution approach. Our method for a nonlinear coupled system with nonlinear CBC is new and it unifies the treatment of many different first-order problems. Examples are included to ensure the validity of the results.

##### MSC:

34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |

34B15 | Nonlinear boundary value problems for ordinary differential equations |

47N20 | Applications of operator theory to differential and integral equations |

##### Keywords:

lower and upper solutions; coupled nonlinear system; coupled nonlinear boundary condition; Arzela-Ascoli theorem; Schauder theorem
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\textit{N. A. Asif} et al., Bound. Value Probl. 2015, Paper No. 134, 9 p. (2015; Zbl 1342.34035)

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