A note on sufficient conditions for the real Jacobian conjecture in R^2
Abstract
The real Jacobian conjecture in \(\mathbb{R}^2\) claims that if \(F=(f,g):\mathbb{R}^2 \to \mathbb{R}^2\) is a polynomial map such that \(\det DF(x,y)\neq 0\) for all \((x,y)\in \mathbb{R}^2\), then \(F\) is globally injective. However, it is known that there exists a counterexample on this conjecture. Since then, various sufficient conditions have been proposed to ensure that the real Jacobian conjecture holds. In this article, we generalize a result in [25] to the quasi-homogeneous case. Moreover, we provide several examples to illustrate the relationships between some existing sufficient conditions regarding this conjecture. For more information and the latex file, see https://ejde.math.txstate.edu/Volumes/2026/12/abstr.html
Fields of Study & Subjects
Advanced Differential Equations and Dynamical Systems
Mathematical Dynamics and Fractals
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Electronic Journal of Differential Equations
- Volume
- 2026
- Issue
- 01-??
- Pages
- 12–12
- Publication date
- 11 February 2026
- Language
- EN