Higher-order delay differential equations with meromorphic solutions

IF 0.5 3区数学 Q3 MATHEMATICS

Analysis Mathematica Pub Date : 2025-09-03 DOI:10.1007/s10476-025-00109-1

Y. Liu, W. L. Liu

引用次数: 0

Abstract

In this paper, we consider the equation

$$\overline{y}\underline{y}+\alpha(x)\frac{y^{(d)}}{y^{2}}=R(x,y)=\frac{H(x, y)}{G(x, y)},$$

where $\alpha(x)$ is a nonzero rational, $H(x,y)$ and $G(x,y)$ are co-prime polynomials of $y$ with rational coefficients. If there exists a non-rational meromorphic solution with $\rho_{2}(y)<1 $, then $\deg_{y}(H)$ and $\deg_{y}(G)$ must satisfy certain conditions.

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具有亚纯解的高阶时滞微分方程

本文考虑方程$$\overline{y}\underline{y}+\alpha(x)\frac{y^{(d)}}{y^{2}}=R(x,y)=\frac{H(x, y)}{G(x, y)},$$，其中$\alpha(x)$是一个非零有理，$H(x,y)$和$G(x,y)$是含有有理系数的$y$的协素数多项式。如果存在一个具有$\rho_{2}(y)<1 $的非有理亚纯解，则$\deg_{y}(H)$和$\deg_{y}(G)$必须满足一定的条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Analysis Mathematica MATHEMATICS-

CiteScore

1.00

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Traditionally the emphasis of Analysis Mathematica is classical analysis, including real functions (MSC 2010: 26xx), measure and integration (28xx), functions of a complex variable (30xx), special functions (33xx), sequences, series, summability (40xx), approximations and expansions (41xx). The scope also includes potential theory (31xx), several complex variables and analytic spaces (32xx), harmonic analysis on Euclidean spaces (42xx), abstract harmonic analysis (43xx). The journal willingly considers papers in difference and functional equations (39xx), functional analysis (46xx), operator theory (47xx), analysis on topological groups and metric spaces, matrix analysis, discrete versions of topics in analysis, convex and geometric analysis and the interplay between geometry and analysis.