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In this article, we mainly use Nevanlinna theory to investigate some special difference equations of malmquist type such as $f^2+{(\Delta_c f)}^2={\beta}^2$, ${f}^2+{(\Delta_cf)}^2=R$, ${f'}^2+{(\Delta_cf)}^2=R$ and $f^2+{\big(f(z+c)\big)}^2=R$, where $\beta$ is a nonzero small function of $f$ and $R$ is a nonzero rational function respectively. These discussions extend one related result due to C.~C.~Yang et al.~in some sense.
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참고문헌 (10)
참고문헌 신청
Wei Chen / 2016 / On solutions to some nonlinear difference and differential equations / 대한수학회지 53(4):835~846
Y. M. Chiang / 2008 / On the Nevanlinna characteristic of $f(z+{\eta})$ and difference equations in the complex plane / Ramanujian J. 16(1):105~129
Y. M. Chiang / 2009 / On the growth of logarithmic differences, difference quotients and logarithmic derivatives of meromorphic functions / Trans. Amer. Math. Soc. 361(7):3767~3791
W. K. Hayman / 1964 / Meromorphic Functions / Clarendon Press
I. Laine / 2007 / Clunie theorem for difference and q-difference polynomials / J. London Math. Soc. 76(3):556~566
Y. M. Chiang / 2008 / On the Nevanlinna characteristic of
Y. M. Chiang / 2009 / On the growth of logarithmic differences, difference quotients and logarithmic derivatives of meromorphic functions / Trans. Amer. Math. Soc. 361(7):3767~3791
W. K. Hayman / 1964 / Meromorphic Functions / Clarendon Press
I. Laine / 2007 / Clunie theorem for difference and q-difference polynomials / J. London Math. Soc. 76(3):556~566
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