Abstract
We study the periodic solutions of the second-order differential equations of the form ẍ ± xn = μ f (t), or ẍ ± |x|n = μ f(t), where n = 4, 5,⋯, f(t) is a continuous T-periodic function such that ∫ 0T f(t)dt = 0, and μ is a positive small parameter. Note that the differential equations ẍ ± xn = μ f(t) are only continuous in t and smooth in x, and that the differential equations ẍ ± |x|n = μ f(t) are only continuous in t and locally-Lipschitz in x.
Original language | English |
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Pages (from-to) | 477-482 |
Journal | Discrete and Continuous Dynamical Systems - Series B |
Volume | 22 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Mar 2017 |
Keywords
- Averaging theory
- Periodic solution
- Second order differential equations