Symmetries and well-defined solutions for a non-linear difference equation
Abstract
In this paper, we apply the similarity method to a non-linear difference equation of order four, where the parameters are non-zero real number sequences and with real initial values. We derive Lie symmetry generators of the difference equation and derive a formula to its well-defined solutions. For special cases of the parameters, we show the existence of periodic solutions. We prove that under certain conditions, every solution converges either to zero or (to a periodic solution). Finally, we introduce the forbidden sets of that difference equation as well as provide some examples that clarify the theoretical results.
Fields of Study & Subjects
Mathematical and Theoretical Epidemiology and Ecology Models
Nonlinear Differential Equations Analysis
Nonlinear Waves and Solitons
Publication details
- Journal / source
- The Journal of Difference Equations and Applications
- Publisher
- Informa UK Limited
- Volume
- 32
- Issue
- 7
- Pages
- 1205–1216
- Publication date
- 13 May 2026
- Language
- EN