On Nonlinear Hahn Difference Equations with Maxima: On Nonlinear Hahn Difference Equations with Maxima - Zhou, Longyun; Wang, JinRong (Qualitative theory of dynamical systems, 2025)
In this paper, we study the first and second order nonlinear Hahn difference equations with maxima. Firstly, we prove the existence and uniqueness of the solutions to the nonlinear Hahn difference equations with the help of theorem of step by step contraction. Then, we obtain a comparison theorem by constructing successive approximation sequences in combination with the weakly Picard operator (WPO). Further, the Ulam’s type stability of the nonlinear Hahn difference equations with maxima are given. Finally, two examples are given to illustrate the theoretical results.