By using asymptotic method, we verify the existence on the slowly growing solutions to second order difference equations discussed by Ishizaki-Yanagihara's Wiman-Valiron method and Ishizaki-Wen's binomial series method. The classical problem on finding conditions on the polynomial coefficients $P_{j}(z) ~(j=0,1,2)$ and $F(z)$ to guarantee that all nontrivial solutions of complex second order difference equation $ P_2(z)f(z+2)+P_1(z)f(z+1)+P_0(z)f(z)=F(z)$ has slowly growing solutions with order $1/2$ is detected.
Zongxuan CHEN
,
Zhibo HUANG
,
Jun WANG
,
Xiumin ZHENG
. DETECTING THE SLOWLY GROWING SOLUTIONS OF SECOND ORDER LINEAR DIFFERENCE EQUATIONS[J]. Acta mathematica scientia, Series B, 2025
, 45(3)
: 837
-854
.
DOI: 10.1007/s10473-025-0306-4
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