Meromorphic solutions of a Riccati differential equation with a doubly periodic coefficient

Shun Shimomura

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3 Citations (Scopus)


We treat a Riccati differential equation w′ + w2 + 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 languageEnglish
Pages (from-to)644-651
Number of pages8
JournalJournal of Mathematical Analysis and Applications
Issue number2
Publication statusPublished - 2005 Apr 15



  • Meromorphic solution
  • Riccati differential equation
  • Value distribution

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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