### Abstract

We consider the existence of positive ω-periodic solutions for the periodic equation x^{′} (t) = a (t) e^{x (t)} x (t) - λ b (t) f (x (t - τ (t))), where a, b ∈ C (R, [0, ∞)) are ω-periodic, ∫_{0}
^{ω} a (t) d t > 0, ∫_{0}
^{ω} b (t) d t > 0, f ∈ C ([0, ∞), [0, ∞)), and f (u) > 0 for u > 0, τ (t) is a continuous ω-periodic function.

Original language | English (US) |
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Pages (from-to) | 581-584 |

Number of pages | 4 |

Journal | Applied Mathematics Letters |

Volume | 23 |

Issue number | 5 |

DOIs | |

State | Published - May 2010 |

### Fingerprint

### Keywords

- Existence
- Fixed index theorem
- Positive periodic solution

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

*Applied Mathematics Letters*,

*23*(5), 581-584. https://doi.org/10.1016/j.aml.2010.01.015

**A note on positive periodic solutions of delayed differential equations.** / Jin, Zhi Long; Wang, Haiyan.

Research output: Contribution to journal › Article

*Applied Mathematics Letters*, vol. 23, no. 5, pp. 581-584. https://doi.org/10.1016/j.aml.2010.01.015

}

TY - JOUR

T1 - A note on positive periodic solutions of delayed differential equations

AU - Jin, Zhi Long

AU - Wang, Haiyan

PY - 2010/5

Y1 - 2010/5

N2 - We consider the existence of positive ω-periodic solutions for the periodic equation x′ (t) = a (t) ex (t) x (t) - λ b (t) f (x (t - τ (t))), where a, b ∈ C (R, [0, ∞)) are ω-periodic, ∫0 ω a (t) d t > 0, ∫0 ω b (t) d t > 0, f ∈ C ([0, ∞), [0, ∞)), and f (u) > 0 for u > 0, τ (t) is a continuous ω-periodic function.

AB - We consider the existence of positive ω-periodic solutions for the periodic equation x′ (t) = a (t) ex (t) x (t) - λ b (t) f (x (t - τ (t))), where a, b ∈ C (R, [0, ∞)) are ω-periodic, ∫0 ω a (t) d t > 0, ∫0 ω b (t) d t > 0, f ∈ C ([0, ∞), [0, ∞)), and f (u) > 0 for u > 0, τ (t) is a continuous ω-periodic function.

KW - Existence

KW - Fixed index theorem

KW - Positive periodic solution

UR - http://www.scopus.com/inward/record.url?scp=77949485003&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77949485003&partnerID=8YFLogxK

U2 - 10.1016/j.aml.2010.01.015

DO - 10.1016/j.aml.2010.01.015

M3 - Article

AN - SCOPUS:77949485003

VL - 23

SP - 581

EP - 584

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

SN - 0893-9659

IS - 5

ER -