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Acta Applicandae Mathematicae

, Volume 159, Issue 1, pp 29–74 | Cite as

Elliptic Quadratic Operator Equations

  • Rasul Ganikhodzhaev
  • Farrukh MukhamedovEmail author
  • Mansoor Saburov
Article
  • 24 Downloads

Abstract

The paper is devoted to the study of elliptic quadratic operator equations over the finite dimensional Euclidean space. We provide necessary and sufficient conditions for the existence of solutions of elliptic quadratic operator equations. The iterative Newton-Kantorovich method for stable solutions is also presented.

Keywords

Elliptic operator Quadratic operator Number of solutions Rank of elliptic operator Stable solution Newton-Kantorovich method 

Mathematics Subject Classification

47H60 47J05 52Axx 52Bxx 

Notes

Acknowledgements

The present work is supported by the UAEU “Start-Up” Grant, No. 31S259.

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  • Rasul Ganikhodzhaev
    • 1
  • Farrukh Mukhamedov
    • 2
    Email author
  • Mansoor Saburov
    • 3
  1. 1.Faculty of Mechanics & MathematicsNational University UzbekistanTashkentUzbekistan
  2. 2.Department of Mathematical Sciences, College of ScienceThe United Arab Emirates UniversityAbu DhabiUAE
  3. 3.Mathematics Department, College of Engineering and TechnologyAmerican University of the Middle EastEgailaKuwait

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