Uniqueness of meromorphic solutions of the difference equation $R_{1}(z)f(z+1)+R_{2}(z)f(z)=R_{3}(z)$
نویسندگان
چکیده
منابع مشابه
On meromorphic solutions of certain type of difference equations
We mainly discuss the existence of meromorphic (entire) solutions of certain type of non-linear difference equation of the form: $f(z)^m+P(z)f(z+c)^n=Q(z)$, which is a supplement of previous results in [K. Liu, L. Z. Yang and X. L. Liu, Existence of entire solutions of nonlinear difference equations, Czechoslovak Math. J. 61 (2011), no. 2, 565--576, and X. G. Qi...
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* Correspondence: [email protected]. com School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P. R. China Full list of author information is available at the end of the article Abstract In this article, we investigate the uniqueness problems of difference operators of two meromorphic functions. Uniqueness of a meromorphic function f and its difference operator with the ...
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We find all nonrational meromorphic solutions of the equation ww′′ − (w′)2 = α(z)w + β(z)w′ + γ (z), where α, β, and γ are rational functions of z. In so doing, we answer a question of Hayman by showing that all such solutions have finite order. Apart from special choices of the coefficient functions, the general solution is not meromorphic and contains movable branch points. For some choices f...
متن کاملon meromorphic solutions of certain type of difference equations
we mainly discuss the existence of meromorphic (entire) solutions of certain type of non-linear difference equation of the form: $f(z)^m+p(z)f(z+c)^n=q(z)$, which is a supplement of previous results in [k. liu, l. z. yang and x. l. liu, existence of entire solutions of nonlinear difference equations, czechoslovak math. j. 61 (2011), no. 2, 565--576, and x. g. qi...
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ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2019
ISSN: 1687-1847
DOI: 10.1186/s13662-019-2194-1