Article
Mathematics
Qiong Wang, Qi Han, Wei Chen
Summary: This paper studies the meromorphic solutions to the generalized Fermat Diophantine functional equations and associated partial differential equations.
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
(2022)
Article
Multidisciplinary Sciences
Nan Li, Lianzhong Yang
Summary: This paper improves and complements the research results of Chen and Laine, and investigates the zero distribution of a linear delay-differential polynomial with small coefficients.
Article
Mathematics, Applied
Elias G. G. Saleeby
Summary: In this article, a system {f, g, h} of meromorphic functions in C-3 that are algebraically dependent is characterized. The algebraic dependence described by space curves of genus zero or genus one is considered, and it is shown that all three functions share a right common factor. Functional and differential equations associated to space curves are defined and the existence and the forms of their complex analytic solutions are studied.
MEDITERRANEAN JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics
Jinyu Fan, Jianbin Xiao, Mingliang Fang
Summary: In this article, the value distribution of differential polynomials is studied and the main theorem is proved. It states that for a polynomial P with degree P >= 3 and a transcendent meromorphic function f, with a small function alpha. If alpha is a constant, it is further required that there exists a constant A not equal to alpha such that P(z) - A has a zero of multiplicity at least 3. Then, for any 0 < epsilon < 1, Tr,f <= kN (1/r, P f-alpha )+ S(r,f), where the value of k depends on the characteristics of P'(z) and alpha.
Article
Mathematics
Pei-Chu Hu, Man-Li Liu
Summary: The study focuses on the properties of integer solutions of delay differential equations with rational coefficients, and demonstrates the accuracy of the results by simplifying the equation form.
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
(2021)
Review
Mathematics
Yuxian Chen, Libing Xie, Hongyan Xu
Summary: This article describes the entire solutions of some partial differential-difference equations and systems. The theorems about the forms of transcendental entire solutions with finite order for high-order partial differential-difference equations (or systems) of the Fermat type with two complex variables are obtained. Additionally, examples are provided to demonstrate the precision of the results to some extent.
JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics
Janne Heittokangas, Katsuya Ishizaki, Kazuya Tohge, Zhi-Tao Wen
Summary: This article introduces the definition and research history of exponential polynomials, discusses some unsolved problems, and explores the applications of exponential polynomials in various fields. Thirteen open problems are also provided to inspire further research.
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
(2023)
Article
Mathematics
Luis Manuel Sanchez Ruiz, Sanjib Kumar Datta, Samten Tamang, Nityagopal Biswas
Summary: In this study, we investigate the growth order of solutions in complex higher order linear differential equations with entire and meromorphic coefficients. We show how this growth is related to the growth of the unknown function's coefficients under certain assumptions, and our findings build upon previous results by Liu, Tu, Shi, Li, Cao, and others.
Article
Mathematics
Yinhao Guo, Kai Liu
Summary: In this paper, we discuss the existence of solutions for Fermat type differential equations and Fermat type difference equations, and provide concise proofs using elliptic functions.
ANNALES POLONICI MATHEMATICI
(2023)
Article
Mathematics
Jun Wang, Xiao Yao, Chengchun Zhang
Summary: The research focuses on the limiting directions of entire or meromorphic functions in Julia sets and their connection to differential polynomials.
ACTA MATHEMATICA SCIENTIA
(2021)
Article
Mathematics, Applied
Pulak Sahoo, Anjan Sarkar
Summary: This paper investigates the value distribution of the differential polynomial for transcendental meromorphic functions, proving an inequality for the Nevanlinna characteristic function. The results improve upon previous research and contribute to the field of mathematics.
Article
Mathematics, Applied
Zhiying He, Jianbin Xiao, Mingliang Fang
Summary: The paragraph discusses the properties and conditions of two transcendental meromorphic functions, as well as their relationship under certain conditions. It extends and improves previous results in the field.
Article
Mathematics, Applied
Goutam Haldar
Summary: This paper investigates the properties of transcendental entire solutions of Fermat-type difference and partial differential-difference equations in C-n using Nevanlinna theory for meromorphic functions in several complex variables. It also provides the precise form of transcendental entire solutions in C-2 with finite order of the Fermat-type partial differential-difference equation and improves upon previous results.
MEDITERRANEAN JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics, Applied
Alireza Khalili Golmankhaneh, Ines Tejado, Hamdullah Sevli, Juan E. Napoles Valdes
Summary: This paper provides a brief summary of fractal calculus, presenting fractal functional differential equations as a mathematical model for phenomena with fractal time and structure. The method of steps and Laplace transform are used to solve fractal retarded, neutral, and renewal delay differential equations with constant coefficients, and the graphs of solutions are provided to illustrate the details.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Mathematics, Applied
Zhiying He, Jinyu Fan, Mingliang Fang
Summary: This paper investigates the value distribution of meromorphic functions in relation to difference polynomials and solves an open problem proposed by Zheng and Chen. By utilizing different methods, we enhance and extend some previous findings by Zheng and Chen, as well as Zhang and Huang.
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION
(2023)
