Mathematical Models for the Study of Resource Systems Based on Functional Operators with Shift

  • Oleksandr Karelin
  • Anna TarasenkoEmail author
  • Viktor Zolotov
  • Manuel Gonzalez-Hernandez
Conference paper


In previous works we proposed a method for the study of systems with one renewable resource. The separation of the individual and the group parameters and the discretization of time led us to scalar linear functional equations with shift. Cyclic models, in which the initial state of the system coincides with the final state, were considered. In this work, we present models for systems with two renewable resources. In modelling, the interactions and the reciprocal influences between these two resources are taken into account. Analysis of the models is carried out in weighted Holder spaces. For cyclic models a method for the solution of the balance equations is proposed. The equilibrium state of the system is found. Some problems for the optimal exploitation of resources of open systems are formulated.


Degenerate kernel Equilibrium state Exploitation of resources Holder space Invertibility Renewable resources 


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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Oleksandr Karelin
    • 1
  • Anna Tarasenko
    • 2
    Email author
  • Viktor Zolotov
    • 3
  • Manuel Gonzalez-Hernandez
    • 1
  1. 1.Department of Industrial EngineeringInstitute of Basic Sciences and Engineering, Hidalgo State Autonomous UniversityPachucaMexico
  2. 2.Department of MathematicsInstitute of Basic Sciences and Engineering, Hidalgo State UniversityPachucaMexico
  3. 3.Department of Economics of Nature-Resource ManagementInstitute for Market Problems and Economic and Ecological Research of the National Academy of Sciences of UkraineOdessaUkraine

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