### Abstract

We treat a Riccati differential equation w′ + w^{2} + p(z) = 0, where p(z) is a nonconstant doubly periodic meromorphic function. Under certain assumptions, every solution is meromorphic in the whole complex plane. We show that the growth order of it is equal to 2, and examine the frequency of α-points and poles. Furthermore, the number of doubly periodic solutions is discussed.

Original language | English |
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Pages (from-to) | 644-651 |

Number of pages | 8 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 304 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2005 Apr 15 |

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### Keywords

- Meromorphic solution
- Riccati differential equation
- Value distribution

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics