On entire solutions of a class of second-order algebraic differential equations
type: Item
instance of: scholarly article
title: On entire solutions of a class of second-order algebraic differential equations
zbMATH Open document ID: 1483.34118
DOI: 10.1134/S0001434621070300
author: A. Ya. Yanchenko
published in: Mathematical Notes
publication date: 2021-08-25T00:00:00Z
review text: Let \(\mathbb{C}(z)\) be the field of rational functions over \(\mathbb{C}\), and let \(\mathbb{C}[\omega_0,\ldots,\omega_n]\) denote the set of polynomials of variables \(\omega_0,\ldots,\omega_n\) over the field of complex numbers. Furthermore, let \(b_0,b_1,b_2\in\mathbb{C}[z]\) with \(b_2\not\equiv 0\) and let \(A\in\mathbb{C}[z,\omega_0,\omega_1,\omega_2]\) such that \(A[z,0,\omega_1,-(b_1/b_2)\omega_1]\not\in\mathbb{C}(z)\). In the paper under review it is shown that if \(y=f(z)\) is a finite-order entire solution of \[ b_2 y'' + b_1 y' + b_0y + y A(z,y,y',y'') =0, \] then there exist \(A_1,A_2\in\mathbb{C}[z]\) and \(B_1,B_2\in\mathbb{C}(z)\) such that \[ f(z)=B_1 e^{A_1} + B_2 e^{A_2}. \]
reviewed by: Risto Korhonen
Mathematics Subject Classification ID: 34M05
Mathematics Subject Classification ID: 34M04
Mathematics Subject Classification ID: 34M10
zbMATH DE Number: 7384991
zbMATH Keywords: algebraic differential equations
zbMATH Keywords: entire functions of finite order
zbMATH Keywords: entire solutions of differential equations
MaRDI profile type: Publication
Wikidata QID: Q115253647
cites work: Q5797273
cites work: Meromorphic solutions of algebraic differential equations
cites work: Q3161232
cites work: Some arithmetic properties of the values of entire functions of finite order and their first derivatives
cites work: On a strengthening of certain theorems of Gelfond on the integer-valuedness of analytic functions
cites work: Q3232414
cites work: Q3765856
full work available at URL: s0001434621070300
OpenAlex ID: W3195390913
description: scientific article; zbMATH DE number 7384991