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Archiv der Mathematik

, Volume 82, Issue 5, pp 442–448 | Cite as

On the transcendental solutions of a certain type of nonlinear differential equations

  • C.-C. YangEmail author
  • P. LiEmail author
Original paper

Abstract.

In this paper, we shall utilize Nevanlinna value distribution theory to study the solvability of transcendental meromorphic function f(z) that satisfies the differential equations of the form: \( f^{2}(z) + b(z)(L(f))^{2} = a(z) \), where L(f) denotes a linear differential polynomial in f, a(z) and b(z) are nonzero small functions of f(z). As an application, the method developed here can be used, for instance, to obtain all the entire solutions of the nonlinear differential equation \( 4f^{3}(z) + 3f''(z) = -\sin3z. \)

Mathematics Subject Classification (2000):

Primary 34A20 30D35. 

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Copyright information

© Birkhäuser-Verlag 2004

Authors and Affiliations

  1. 1.Department of MathematicsThe Hong Kong University of Science and TechnologyHong KongP. R. China
  2. 2.Department of MathematicsUniversity of Science and Technology of ChinaHefei, AnhuiP. R. China

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