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On meromorphic solutions of certain nonlinear differential equations

Published online by Cambridge University Press:  17 April 2009

J. Heittokangas ,
R. Korhonen  and
I. Laine
J. Heittokangas
Affiliation:
Department of Mathematics, University of Joensuu, P.O. Box 111, FIN-80101 Joensuu, Finland, e-mail: heittoka@cc.joensuu.fi, rkorhone@cc.joensuu.fi, ilpo.laine@joensuu.fi
R. Korhonen
Affiliation:
Department of Mathematics, University of Joensuu, P.O. Box 111, FIN-80101 Joensuu, Finland, e-mail: heittoka@cc.joensuu.fi, rkorhone@cc.joensuu.fi, ilpo.laine@joensuu.fi
I. Laine
Affiliation:
Department of Mathematics, University of Joensuu, P.O. Box 111, FIN-80101 Joensuu, Finland, e-mail: heittoka@cc.joensuu.fi, rkorhone@cc.joensuu.fi, ilpo.laine@joensuu.fi
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In this paper, we consider the growth of meromorphic solutions of nonlinear differential equations of the form L (f) + P (z, f) = h (z), where L (f) denotes a linear differential polynomial in f, P (z, f) is a polynomial in f, both with small meromorphic coefficients, and h (z) is a meromorphic function. Specialising to L (f) − p (z) fn = h (z), where p (z) is a small meromorphic function, we consider the uniqueness of meromorphic solutions with few poles only. Our results complement earlier ones due to C.-C. Yang.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 66 , Issue 2 , October 2002 , pp. 331 - 343
Copyright
Copyright © Australian Mathematical Society 2002

References

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