Multiple nonnegative solutions of systems with coupled nonlinear boundary conditions.

*(English)*Zbl 1312.34060The authors present a theory for the existence of positive solution for a fairly general class of systems of ODEs subject to nonlinear, nonlocal boundary conditions (BCs). Using the theory of fixed point index, they investigated the existence and multiplicity of positive solutions for the perturbed Hammerstein integral equations. Then, the results are applied to coupled systems of boundary value problems.

Reviewer: Yuqiang Feng (Wuhan)

##### MSC:

34B18 | Positive solutions to nonlinear boundary value problems for ordinary differential equations |

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

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

47H30 | Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.) |

##### Keywords:

fixed point index; cone; nonnegative solution; nonlinear boundary conditions; coupled boundary conditions
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\textit{G. Infante} and \textit{P. Pietramala}, Math. Methods Appl. Sci. 37, No. 14, 2080--2090 (2014; Zbl 1312.34060)

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