Algebraic Systems with Positive Coefficients and Positive Solutions

The paper is devoted to the existence, uniqueness and nonuniqueness of positive solutions to nonlinear algebraic systems of equations with positive coefficients. Such systems appear in large numbers of applications, such as steady-state equations in continuous and discrete dynamical models, Dirichle...
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Autor*in:	Ana Maria Acu [verfasserIn] Ioan Raşa [verfasserIn] Ancuţa Emilia Şteopoaie [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	Brouwer’s fixed point theorem Krasnoselskii’s fixed point theorem nonlinear algebraic systems of equations

Übergeordnetes Werk:	In: Mathematics - MDPI AG, 2013, 10(2022), 8, p 1327
Übergeordnetes Werk:	volume:10 ; year:2022 ; number:8, p 1327

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/math10081327

Katalog-ID:	DOAJ034070230

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allfieldsSound	10.3390/math10081327 doi (DE-627)DOAJ034070230 (DE-599)DOAJ5c7cb4b9112a4bd3bc807ccffcb33420 DE-627 ger DE-627 rakwb eng QA1-939 Ana Maria Acu verfasserin aut Algebraic Systems with Positive Coefficients and Positive Solutions 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The paper is devoted to the existence, uniqueness and nonuniqueness of positive solutions to nonlinear algebraic systems of equations with positive coefficients. Such systems appear in large numbers of applications, such as steady-state equations in continuous and discrete dynamical models, Dirichlet problems, difference equations, boundary value problems, periodic solutions and numerical solutions for differential equations. We apply Brouwer’s fixed point theorem, Krasnoselskii’s fixed point theorem and monotone iterative methods in order to extend some known results and to obtain new results. We relax some hypotheses used in the literature concerning the strict monotonicity of the involved functions. We show that, in some cases, the unique positive solution can be obtained by a monotone increasing iterative method or by a monotone decreasing iterative method. As a consequence of one of our results, we recover the existence of a non-negative solution of the Leontief system and describe a monotone iterative method to find it. Brouwer’s fixed point theorem Krasnoselskii’s fixed point theorem nonlinear algebraic systems of equations Mathematics Ioan Raşa verfasserin aut Ancuţa Emilia Şteopoaie verfasserin aut In Mathematics MDPI AG, 2013 10(2022), 8, p 1327 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:10 year:2022 number:8, p 1327 https://doi.org/10.3390/math10081327 kostenfrei https://doaj.org/article/5c7cb4b9112a4bd3bc807ccffcb33420 kostenfrei https://www.mdpi.com/2227-7390/10/8/1327 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 10 2022 8, p 1327
language	English
source	In Mathematics 10(2022), 8, p 1327 volume:10 year:2022 number:8, p 1327
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topic_title	QA1-939 Algebraic Systems with Positive Coefficients and Positive Solutions Brouwer’s fixed point theorem Krasnoselskii’s fixed point theorem nonlinear algebraic systems of equations
topic	misc QA1-939 misc Brouwer’s fixed point theorem misc Krasnoselskii’s fixed point theorem misc nonlinear algebraic systems of equations misc Mathematics
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title	Algebraic Systems with Positive Coefficients and Positive Solutions
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title_auth	Algebraic Systems with Positive Coefficients and Positive Solutions
abstract	The paper is devoted to the existence, uniqueness and nonuniqueness of positive solutions to nonlinear algebraic systems of equations with positive coefficients. Such systems appear in large numbers of applications, such as steady-state equations in continuous and discrete dynamical models, Dirichlet problems, difference equations, boundary value problems, periodic solutions and numerical solutions for differential equations. We apply Brouwer’s fixed point theorem, Krasnoselskii’s fixed point theorem and monotone iterative methods in order to extend some known results and to obtain new results. We relax some hypotheses used in the literature concerning the strict monotonicity of the involved functions. We show that, in some cases, the unique positive solution can be obtained by a monotone increasing iterative method or by a monotone decreasing iterative method. As a consequence of one of our results, we recover the existence of a non-negative solution of the Leontief system and describe a monotone iterative method to find it.
abstractGer	The paper is devoted to the existence, uniqueness and nonuniqueness of positive solutions to nonlinear algebraic systems of equations with positive coefficients. Such systems appear in large numbers of applications, such as steady-state equations in continuous and discrete dynamical models, Dirichlet problems, difference equations, boundary value problems, periodic solutions and numerical solutions for differential equations. We apply Brouwer’s fixed point theorem, Krasnoselskii’s fixed point theorem and monotone iterative methods in order to extend some known results and to obtain new results. We relax some hypotheses used in the literature concerning the strict monotonicity of the involved functions. We show that, in some cases, the unique positive solution can be obtained by a monotone increasing iterative method or by a monotone decreasing iterative method. As a consequence of one of our results, we recover the existence of a non-negative solution of the Leontief system and describe a monotone iterative method to find it.
abstract_unstemmed	The paper is devoted to the existence, uniqueness and nonuniqueness of positive solutions to nonlinear algebraic systems of equations with positive coefficients. Such systems appear in large numbers of applications, such as steady-state equations in continuous and discrete dynamical models, Dirichlet problems, difference equations, boundary value problems, periodic solutions and numerical solutions for differential equations. We apply Brouwer’s fixed point theorem, Krasnoselskii’s fixed point theorem and monotone iterative methods in order to extend some known results and to obtain new results. We relax some hypotheses used in the literature concerning the strict monotonicity of the involved functions. We show that, in some cases, the unique positive solution can be obtained by a monotone increasing iterative method or by a monotone decreasing iterative method. As a consequence of one of our results, we recover the existence of a non-negative solution of the Leontief system and describe a monotone iterative method to find it.
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title_short	Algebraic Systems with Positive Coefficients and Positive Solutions
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Algebraic Systems with Positive Coefficients and Positive Solutions

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