### Abstract

In this work, the authors consider the boundary value problem {(y^{″} + a (t) y = g (t) f (y), 0 ≤ t ≤ 2 π,; y (0) = y (2 π), y^{′} (0) = y^{′} (2 π),) and establish the existence of nonnegative solutions in the case where the associated Green's function may have zeros. The results are illustrated with an example.

Original language | English (US) |
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Pages (from-to) | 176-180 |

Number of pages | 5 |

Journal | Applied Mathematics Letters |

Volume | 21 |

Issue number | 2 |

DOIs | |

State | Published - Feb 1 2008 |

### Keywords

- Existence of nonnegative solutions
- Krasnosel'skii's theorem
- Periodic boundary value problem
- Vanishing Green's function

### ASJC Scopus subject areas

- Applied Mathematics

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## Cite this

Graef, J. R., Kong, L., & Wang, H. (2008). A periodic boundary value problem with vanishing Green's function.

*Applied Mathematics Letters*,*21*(2), 176-180. https://doi.org/10.1016/j.aml.2007.02.019