Analytical approaches for growth models in economics

Polat G. G., Özer T.

Quaestiones Mathematicae, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2023
  • Doi Number: 10.2989/16073606.2023.2181881
  • Journal Name: Quaestiones Mathematicae
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Keywords: Optimal control problem, Prelle-Singer method, Lie symmetries, Jacobi's last multipliers, lambda-symmetries, Hamiltonians, Darboux polynomials
  • Istanbul Technical University Affiliated: Yes


This study deals with the group-theoretical analysis of nonlinear optimal control problems called the optimal growth model with the environmental asset and capitalist decision model of endogenous growth, which are expressed in terms of the current and present value Hamiltonian functions. The first-order conditions for optimal control problems based on Pontryagin’s maximum principle are considered. In addition, Lie point symmetries and their relation with the Prelle-Singer, λ-symmetries, adjoint symmetries, Darboux polynomials, and Jacobi’s last multiplier approaches are studied by analyzing the coupled nonlinear first-order ordinary differential equations corresponding to the first-order conditions. For both current and present Hamiltonian cases, the first integrals and the corresponding analytical (closed-form) solutions and graphical representations for the optimal control problems are represented.