2013/07/30 by Fengying Li, Li, Fengying, Shiqing Zhang +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1307.8002
openalex publication_date 2013/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We try to generalize a result of M. Willem on forced periodic oscillations which required the assumption that the forced potential is periodic on spatial variables. In this paper, we only assume its integral on the time variable is periodic, and so we extend the result to cover the forced pendulum equation. We apply the direct variational minimizing method and Rabinowtz's saddle point theorem to study the periodic solution when the integral of the potential on the time variable is periodic.