On entire solutions of two kinds of quadratic trinomial Fermat type functional equations

2025/10/15 by Xiang, Xuxu, Long, Jianren
#30D35 #39B32 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.13492

Abstract

The existence of entire solutions to quadratic trinomial Fermat type differential-difference equations and \(q\)-difference differential equations involving second-order derivatives is studied by using Nevanlinna theory, and the exact form of entire solutions of the equations mentioned above is founded. Furthermore, some examples are given to show these results.

Citations

• On meromorphic solutions of functional equations of Fermat type
• Holomorphic curves with shift-invariant hyperplane preimages
• On the transcendental solutions of a certain type of nonlinear differential equations

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