Applications of λ-truncations to the study of local and global solvability of nonlinear equations


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Authors

  • Aram Arutyunov
  • Sergey Zhukovskiy

Abstract

In this paper, we consider the equation mceclip1.png in a neighbourhood of a given point mceclip2.png, 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 λ-truncation of F at mceclip3.png¯ belongs to the considered class of polynomial mappings then for every mceclip0-b63ced4048d7d21fc4fc2e03ddac41a8.png close to mceclip1-7dfb53f53f06342c1858193b2c1d4ca3.png there exists a solution to the equation mceclip4.png that is close to mceclip2.png. For polynomial mappings satisfying the regularity conditions we study their stability to bounded continuous perturbations.

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Published

2024-04-08

How to Cite

Arutyunov, A., & Zhukovskiy, S. (2024). Applications of λ-truncations to the study of local and global solvability of nonlinear equations. Eurasian Mathematical Journal, 15(1). Retrieved from https://emj.enu.kz/index.php/main/article/view/4

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