Elliptic Quadratic Operator Equations

Rasul Ganikhodzhaev; Farrukh Mukhamedov; Mansoor Saburov

doi:10.1007/s10440-018-0183-0

Elliptic Quadratic Operator Equations

Rasul Ganikhodzhaev, Farrukh Mukhamedov, Mansoor Saburov

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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.

Original language	English
Pages (from-to)	29-74
Number of pages	46
Journal	Acta Applicandae Mathematicae
Volume	159
Issue number	1
DOIs	https://doi.org/10.1007/s10440-018-0183-0
Publication status	Published - Feb 15 2019

Keywords

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

ASJC Scopus subject areas

Applied Mathematics

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10.1007/s10440-018-0183-0

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title = "Elliptic Quadratic Operator Equations",

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

author = "Rasul Ganikhodzhaev and Farrukh Mukhamedov and Mansoor Saburov",

note = "Funding Information: The present work is supported by the UAEU “Start-Up” Grant, No. 31S259. Publisher Copyright: {\textcopyright} 2018, Springer Nature B.V.",

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AU - Ganikhodzhaev, Rasul

AU - Mukhamedov, Farrukh

AU - Saburov, Mansoor

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N2 - 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.

AB - 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.

KW - Elliptic operator

KW - Newton-Kantorovich method

KW - Number of solutions

KW - Quadratic operator

KW - Rank of elliptic operator

KW - Stable solution

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Elliptic Quadratic Operator Equations

Abstract

Keywords

ASJC Scopus subject areas

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