## Abstract

We propose an approach for studying positivity of Green’s operators of a nonlocal boundary value problem for the system of n linear functional differential equations with the boundary conditions n_{i}x_{i} − Σ^{n}_{j=1} m_{ij}x_{j} = β_{i}, i = 1,...,n, where n_{i} and m_{ij} are linear bounded “local” and “nonlocal” functionals, respectively, from the space of absolutely continuous functions. For instance, (Formula presented.) can be considered. It is demonstrated that the positivity of Green’s operator of nonlocal problem follows from the positivity of Green’s operator for auxiliary “local” problem which consists of a “close” equation and the local conditions n_{i}x_{i} = α_{i}, i = 1,...,n.

Original language | English |
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Pages (from-to) | 621-638 |

Number of pages | 18 |

Journal | Mathematica Bohemica |

Volume | 139 |

Issue number | 4 |

State | Published - 2014 |

## Keywords

- Differential inequalities
- Functional differential equation
- Fundamental matrix
- Nonlocal boundary value problem
- Positivity of Green’s operator

## All Science Journal Classification (ASJC) codes

- Mathematics(all)