IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i8p1327-d795372.html
   My bibliography  Save this article

Algebraic Systems with Positive Coefficients and Positive Solutions

Author

Listed:
  • Ana Maria Acu

    (Department of Mathematics and Informatics, Lucian Blaga University of Sibiu, Str. Dr. I. Ratiu, No. 5-7, 550012 Sibiu, Romania
    These authors contributed equally to this work.)

  • Ioan Raşa

    (Department of Mathematics, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania
    These authors contributed equally to this work.)

  • Ancuţa Emilia Şteopoaie

    (Department of Mathematics, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Ana Maria Acu & Ioan Raşa & Ancuţa Emilia Şteopoaie, 2022. "Algebraic Systems with Positive Coefficients and Positive Solutions," Mathematics, MDPI, vol. 10(8), pages 1-10, April.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1327-:d:795372
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/8/1327/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/8/1327/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fuad Aleskerov & Hasan Ersel & Dmitri Piontkovski, 2011. "Linear Algebra for Economists," Springer Texts in Business and Economics, Springer, number 978-3-642-20570-5, October.
    2. Moghadam, Amin Abrishami & Soheili, Ali R. & Bagherzadeh, Amir Saboor, 2022. "Numerical solution of fourth-order BVPs by using Lidstone-collocation method," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    3. Yongqiang Du & Guang Zhang & Wenying Feng, 2016. "Existence of Positive Solutions for a Class of Nonlinear Algebraic Systems," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-7, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Giorgio Giorgi, 2022. "Nonsingular M-matrices: a Tour in the Various Characterizations and in Some Related Classes," DEM Working Papers Series 206, University of Pavia, Department of Economics and Management.
    2. Dang, Quang A. & Dang, Quang Long & Ngo, T. Kim Quy, 2024. "Numerical methods of fourth, sixth and eighth orders convergence for solving third order nonlinear ODEs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 397-414.
    3. Georgios Angelidis & Charalambos Bratsas & Georgios Makris & Evangelos Ioannidis & Nikos C. Varsakelis & Ioannis E. Antoniou, 2021. "Global Value Chains of COVID-19 Materials: A Weighted Directed Network Analysis," Mathematics, MDPI, vol. 9(24), pages 1-19, December.
    4. Escobar, Juan F., 2013. "Equilibrium analysis of dynamic models of imperfect competition," International Journal of Industrial Organization, Elsevier, vol. 31(1), pages 92-101.
    5. Giorgio Giorgi, 2019. "Nonnegative Square Matrices: Irreducibility, Reducibility, Primitivity and Some Economic Applications," DEM Working Papers Series 175, University of Pavia, Department of Economics and Management.
    6. Boris Abeli Pekarou Pemi & Donatien Njomo & René Tchinda & Jean Calvin Seutche & Daniel Roméo Kamta Legue & Mahamat Hassane Babikir & Venant Sorel Chara-Dackou, 2023. "Modeling and Quantitative Analysis in the Energy–Food–Water–Waste Nexus (EF2W): Case Study in Cameroon," Sustainability, MDPI, vol. 15(11), pages 1-21, May.
    7. Giorgio Giorgi, 2017. "Various Proofs of the Sylvester Criterion for Quadratic Forms," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 9(6), pages 55-66, December.
    8. Hadeel Alharbi & Houssem Jerbi & Mourad Kchaou & Rabeh Abbassi & Theodore E. Simos & Spyridon D. Mourtas & Vasilios N. Katsikis, 2023. "Time-Varying Pseudoinversion Based on Full-Rank Decomposition and Zeroing Neural Networks," Mathematics, MDPI, vol. 11(3), pages 1-14, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1327-:d:795372. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.