Meromorphic Solutions of Nonlinear Systems of Fermat Type

Article Mathematics

FERMAT AND MALMQUIST TYPE MATRIX DIFFERENTIAL EQUATIONS

Y. X. Li et al.

Summary: This paper discusses two types of matrix differential equations: Fermat type and Malmquist type. By solving systems of nonlinear differential equations, the properties of the meromorphic matrix solutions for the above matrix differential equations are obtained. In addition, a type of nonlinear differential equation called Bi-Fermat differential equation is also considered.

ANALYSIS MATHEMATICA (2023)

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Article Mathematics, Applied

On Meromorphic Solutions of the Fermat-Type Functional Equation f(z)n + f(z plus c)m = eαz+β

Feng Lu et al.

Summary: This paper studies the existence of meromorphic solutions with hyper-order strictly less than 1 to the functional equation in the complex plane. An example is provided to demonstrate the sharpness of the condition on hyper-order for meromorphic solutions.

MEDITERRANEAN JOURNAL OF MATHEMATICS (2022)

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Article Mathematics, Applied

Transcendental entire solutions for several quadratic binomial and trinomial PDEs with constant coefficients

Hong Yan Xu et al.

Summary: This article discusses the existence of entire solutions of quadratic binomial and trinomial partial differential equations with constant coefficients. The authors established a series of theorems on the forms of finite order transcendental entire solutions for these equations, which generalize and improve upon previous theorems. Examples are provided to demonstrate the precise existence conditions and forms of transcendental entire solutions with finite order for such equations.

ANALYSIS AND MATHEMATICAL PHYSICS (2022)

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Article Mathematics, Applied