Article no.10

A Method of Lower and Upper Solutions for Control Problems and Application to a Model of Bone Marrow TransplantationResearch Paper, September 24, 2023 / Lorand Gabriel Parajdi

Published in International Journal of Applied Mathematics and Computer Science (AMCS) 33(3), 409-418, DOI: 10.34768/amcs-2023-0029,  2023.

  The full paper is available on the International Journal of Applied Mathematics and Computer Science (AMCS) website:   or

Authors: Lorand Gabriel Parajdi1,2, Radu Precup3,4 and Ioan Ștefan Haplea5

1 Department of Mathematics, West Virginia University, Morgantown, WV, USA 2 Department of Mathematics, “Babeş–Bolyai” University, Cluj-Napoca, Romania 3 Institute of Advanced Studies in Science and Technology, “Babeș-Bolyai” University, Cluj-Napoca, Romania 4 “Tiberiu Popoviciu” Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, Romania 5 Department of Internal Medicine, “Iuliu Hațieganu” University of Medicine and Pharmacy, Cluj-Napoca, Romania

Abstract: A lower and upper solution method is introduced for control problems related to abstract operator equations. The method is illustrated on a control problem for the Lotka-Volterra model with seasonal harvesting and applied to a control problem of cell evolution after bone marrow transplantation.

Keywords: control problem; lower and upper solutions; fixed point; approximation algorithm; numerical solution; medical application.

Cite As: Parajdi LG, Precup R, Haplea IȘ. A method of lower and upper solutions for control problems and application to a model of bone marrow transplantation. International Journal of Applied Mathematics and Computer Science. 2023; 33(3): 409-418.

This work of the first author was supported by the project “The Development of Advanced and Applicative Research Competencies in the Logic of STEAM + Health” (POCU/993/6/13/153310), a project co-financed by the European Social Fund through the Romanian Operational Programme ‘Human Capital’, 2014-2020. For more details about the project, please visit the project website: