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Entire solutions of q-difference equations and value distribution of q-difference polynomials

100%
Zhang J., Yang L.
Annales Polonici Mathematici
|
2013
|
tom 109
|
nr 1
39-46
EN
We investigate the existence and uniqueness of entire solutions of order zero of the nonlinear q-difference equation of the form fⁿ(z) + L(z) = p(z), where p(z) is a polynomial and L(z) is a linear differential-q-difference polynomial of f with small growth coefficients. We also study the zeros distribution of some special type of q-difference polynomials.
2
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Entire functions that share values or small functions with their derivatives

81%
Li S., Gao Z., Zhang J.
Annales Polonici Mathematici
|
2012
|
tom 104
|
nr 1
1-11
EN
We investigate the uniqueness of entire functions sharing values or small functions with their derivatives. One of our results gives a necessary condition on the Nevanlinna deficiency of the entire function f sharing one nonzero finite value CM with its derivative f'. Some applications of this result are provided. Finally, we prove some further results on small function sharing.
3
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Distribution of zeros and shared values of difference operators

81%
Zhang J., Gao Z., Li S.
Annales Polonici Mathematici
|
2011
|
tom 102
|
nr 3
213-221
EN
We investigate the distribution of zeros and shared values of the difference operator on meromorphic functions. In particular, we show that if f is a transcendental meromorphic function of finite order with a small number of poles, c is a non-zero complex constant such that $Δ^k_cf ≠ 0$ for n ≥ 2, and a is a small function with respect to f, then $fⁿΔ^k_cf$ equals a (≠ 0,∞) at infinitely many points. Uniqueness of difference polynomials with the same 1-points or fixed points is also proved.
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