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Title of Journal: Acta. Math. Sin.-English Ser.

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Abbravation: Acta Mathematica Sinica, English Series

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Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society

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Exponential polynomials as solutions of certain nonlinear difference equations

Authors: Zhi Tao Wen, Janne Heittokangas, Ilpo Lain,

Publish Date: 2012/01/19
Volume: 28, Issue:7, Pages: 1295-1306
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Recently, C.-.C. Yang and I. Laine have investigated finite order entire solutions f of nonlinear differential-difference equations of the form f n + L(z, f) = h, where n ≥ 2 is an integer. In particular, it is known that the equation f(z)2 +q(z)f(z +1) = p(z), where p(z),q(z) are polynomials, has no transcendental entire solutions of finite order. Assuming that Q(z) is also a polynomial and c ∈ ℂ, equations of the form f(z) n +q(z)eQ(z) f(z +c) = p(z) do posses finite order entire solutions. A classification of these solutions in terms of growth and zero distribution will be given. In particular, it is shown that any exponential polynomial solution must reduce to a rather specific form. This reasoning relies on an earlier paper due to N. Steinmetz.



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