The growth of meromorphic solutions for q−difference Painlevé IV equation

Peng, Chang-Wen; Huang, Huawei

doi:10.1016/j.jmaa.2020.124485

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“…Peng and Huang [12] considered the growth problem for transcendental meromorphic solutions of qdifference Painlevé IV equation, and obtained the following result.…”

Section: Theorem 1 ([11])mentioning

confidence: 99%

On existence of meromorphic solutions for nonlinear q-difference equation

Peng¹,

Huang²,

Tao³

2023

ScienceAsia

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In this paper, we mainly consider the existence of meromorphic solutions of nonlinear q-difference equation of typewhere the right-hand side is irreducible, P(z, f (z)) and Q(z, f (z)) are polynomials in f with rational coefficients, and q is a nonzero complex constant. We obtain that such equation has no transcendental meromorphic solution when |q| = 1 and m = degAnd we investigate the growth of transcendental meromorphic solutions of nonlinear q-difference equation and find lower bounds for their characteristic functions for transcendental meromorphic solutions of such equation for the case |q| ̸ = 1.

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“…Peng and Huang [12] considered the growth problem for transcendental meromorphic solutions of qdifference Painlevé IV equation, and obtained the following result.…”

Section: Theorem 1 ([11])mentioning

confidence: 99%