Abstract
We consider the class of differential equations \( y^{(k)}+\Sigma_{k- 2}^{\nu=1}A_{\nu}y^{(\nu)}+A_0(z)y=0\ {\rm where}\ A_{1},\dots,A_{k- 2}\) are constants, k ≥ 3 and where A0(z) is a non-constant periodic entire function, which is a rational function of e z. In this paper we develop a method that enables us to decide if this equation can have solutions with few zeros, and we also present the construction of these solutions.
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Baesch, A. On the Explicit Determination of Certain Solutions of Periodic Differential Equations of Higher Order. Results. Math. 29, 43–55 (1996). https://doi.org/10.1007/BF03322203
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DOI: https://doi.org/10.1007/BF03322203