Geodesic
Applications of $\lambda$-truncations to the study of local and global solvability of nonlinear equations
Eurasian mathematical journal, Tome 15 (2024) no. 1, pp. 23-33

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In this paper, we consider the equation $F(x)=y$ in a neighbourhood of a given point $\bar{x}$, where $F$ is a given continuous mapping between finite-dimensional real spaces. We study a class of polynomial mappings and show that these polynomials satisfy certain regularity assumptions. We show that if a $\lambda$-truncation of $F$ at $\bar{x}$ belongs to the considered class of polynomial mappings then for every y close to $F(\bar{x})$ there exists a solution to the equation $F(x) = y$ that is close to $\bar{x}$. For polynomial mappings satisfying the regularity conditions we study their stability to bounded continuous perturbations. 
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     author = {A. V. Arutyunov and S. E. Zhukovskiy},
     title = {Applications of $\lambda$-truncations to the study of local and global solvability of nonlinear equations},
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A. V. Arutyunov; S. E. Zhukovskiy. Applications of $\lambda$-truncations to the study of local and global solvability of nonlinear equations. Eurasian mathematical journal, Tome 15 (2024) no. 1, pp. 23-33. http://geodesic.mathdoc.fr/item/EMJ_2024_15_1_a1/