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On meromorphic solutions of functional-differential equations
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 65 / Issue 1 / February 2022
- Published online by Cambridge University Press:
- 10 February 2022, pp. 263-278
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We consider meromorphic solutions of functional-differential equations
\[ f^{(k)}(z)=a(f^{n}\circ g)(z)+bf(z)+c, \]where $n,\,~k$
are two positive integers. Firstly, using an elementary method, we describe the forms of $f$
and $g$
when $f$
is rational and $a(\neq 0)$
, $b$
, $c$
are constants. In addition, by employing Nevanlinna theory, we show that $g$
must be linear when $f$
is transcendental and $a(\neq 0)$
, $b$
, $c$
are polynomials in $\mathbb {C}$
.
ON UNICITY OF MEROMORPHIC SOLUTIONS TO DIFFERENCE EQUATIONS OF MALMQUIST TYPE
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 93 / Issue 1 / February 2016
- Published online by Cambridge University Press:
- 05 August 2015, pp. 92-98
- Print publication:
- February 2016
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- Article
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In this note, we prove a uniqueness theorem for finite-order meromorphic solutions to a class of difference equations of Malmquist type. Such solutions
$f$ are uniquely determined by their poles and the zeros of 
$f-e_{j}$ (counting multiplicities) for two finite complex numbers 
$e_{1}\neq e_{2}$.
