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On entire solutions of a certain type of nonlinear differential equation

Published online by Cambridge University Press:  17 April 2009

Chung-Chun Yang
Chung-Chun Yang
Affiliation:
Department of Mathematics, The Hong Kong University of Science and Technology, Kowloon, Hong Kong, China
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Abstract

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In this note, we shall study, via Nevanlinna's value distribution theory, the uniqueness of transcendental entire solutions of the following type of nonlinear differential equation: (*) L (f (z)) – p (z) fn(z) = h (z), where L (f) denotes a linear differential polynomial in f with polynomials as its co-efficients, p (z) a polynomial (≢ 0), h an entire function, and n an integer ≥ 3. We show that if the equation (*) has a finite order transcendental entire solution, then it must be unique, unless L (f) ≡ 0.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 64 , Issue 3 , December 2001 , pp. 377 - 380
Copyright
Copyright © Australian Mathematical Society 2001

References

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