Abstract
The optimal control problems in economic growth theory are analyzed by considering the Pontryagin's maximum principle for both current and present value Hamiltonian functions based on the theory of Lie groups. As a result of these necessary conditions, two coupled first-order differential equations are obtained for two different economic growth models. The first integrals and the analytical solutions (closed-form solutions) of two different economic growth models are analyzed via the group theory including Lie point symmetries, Jacobi last multiplier, Prelle-Singer method,_-symmetry and the mathematical relations among them.
| Original language | English |
|---|---|
| Pages (from-to) | 2853-2876 |
| Number of pages | 24 |
| Journal | Discrete and Continuous Dynamical Systems - Series S |
| Volume | 13 |
| Issue number | 10 |
| DOIs | |
| Publication status | Published - Oct 2020 |
Bibliographical note
Publisher Copyright:© 2020 American Institute of Mathematical Sciences. All rights reserved.
Keywords
- Closed-form solutions
- Jacobi last multipliers
- Lie point symmetries
- Optimal control
- _-symmetries