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Uniqueness of meromorphic solutions of a certain type of difference equations

Jun-Fan Chen|Shu-Qing Lin
대한수학회 (The Korean Mathematical Society)|2022.07|대한수학회보 (Bulletin of the KMS)|제59권 제4호|pp. 827-841|DOI 10.4134/BKMS.b210490

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키워드

Nevanlinna theoryfinite orderDifference equationtranscendental meromorphic solution
주제분류수학

초록

In this paper, we study the uniqueness of two finite order transcendental meromorphic solutions $f(z)$ and $g(z)$ of the following complex difference equation $$A_{1}(z)f(z+1)+A_{0}(z)f(z)=F(z)e^{\alpha(z)}$$ when they share 0, $\infty$ CM, where $A_{1}(z),$ $A_{0}(z),$ $F(z)$ are non-zero polynomials, $\alpha(z)$ is a polynomial. Our result generalizes and complements some known results given recently by Cui and Chen, Li and Chen. Examples for the precision of our result are also supplied.

Abstract

In this paper, we study the uniqueness of two finite order transcendental meromorphic solutions $f(z)$ and $g(z)$ of the following complex difference equation $$A_{1}(z)f(z+1)+A_{0}(z)f(z)=F(z)e^{\alpha(z)}$$ when they share 0, $\infty$ CM, where $A_{1}(z),$ $A_{0}(z),$ $F(z)$ are non-zero polynomials, $\alpha(z)$ is a polynomial. Our result generalizes and complements some known results given recently by Cui and Chen, Li and Chen. Examples for the precision of our result are also supplied.

참고문헌 (19)

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