## Abstract

Consider the n-dimensional nonautonomous system ẋ(t) = A(t)G(x(t)) − B(t)F(x(t − τ(t))) Let u = (u_{1},…,u_{n}),(Formula Presented.). Under some quite general conditions, we prove that either F_{0} = 0 and F_{∞} = ∞, or F_{0} = ∞ and F_{∞} = 0, guarantee the existence of positive periodic solutions for the system for all λ > 0. Furthermore, we show that F_{0} = F_{∞} = 0, or F_{∞} = F_{∞} = ∞ guarantee the multiplicity of positive periodic solutions for the system for sufficiently large, or small λ, respectively. We also establish the nonexistence of the system when either F_{0} and F_{∞} > 0, or F_{0} and F_{∞}, < for sufficiently large, or small λ, respectively. We shall use fixed point theorems in a cone.

Original language | English (US) |
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Pages (from-to) | 310-325 |

Number of pages | 16 |

Journal | Results in Mathematics |

Volume | 48 |

Issue number | 3-4 |

DOIs | |

State | Published - Nov 1 2005 |

## Keywords

- existence
- fixed point theorem
- positive periodic solutions

## ASJC Scopus subject areas

- Mathematics (miscellaneous)
- Applied Mathematics