Periodic solutions of Poisson equation
Abstract
In this paper, we prove that for a continuous periodic function $f$ from $\mathbb{R}^{n}$ to ${\mathbb{R}}$, the generalized bounded distribution solution $u$ of the Poisson equation $\Delta u=f$ is also periodic. Furthermore, $u$ is continuously differentiable and $u'$ is also periodic. While high-dimensional primitive function problems for recurrent functions, including almost periodic and almost automorphic functions, have been studied in recent years, this paper presents the first results concerning high-dimensional primitive function problems of periodic functions.
Fields of Study & Subjects
Nonlinear Differential Equations Analysis
Differential Equations and Boundary Problems
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- International Journal of Mathematical Analysis
- Volume
- 20
- Issue
- 1
- Pages
- 1–10
- Publication date
- 1 January 2026
- Language
- EN