By looking at the situation when the coefficients $P_{j}(z)$ $(j=1,2,\cdots,n-1)$ (or most of them) are exponential polynomials, we investigate the fact that all nontrivial solutions to higher order differential equations $f^{(n)}+P_{n-1}(z)f^{(n-1)}+\cdots+P_{0}(z)f=0$ are of infinite order. An exponential polynomial coefficient plays a key role in these results.
Zhibo Huang
,
Minwei Luo
,
Zongxuan Chen
. THE GROWTH OF SOLUTIONS TO HIGHER ORDER DIFFERENTIAL EQUATIONS WITH EXPONENTIAL POLYNOMIALS AS ITS COEFFICIENTS*[J]. Acta mathematica scientia, Series B, 2023
, 43(1)
: 439
-449
.
DOI: 10.1007/s10473-023-0124-5
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