PERIODIC SOLUTIONS OF SOME CLASSES OF CONTINUOUS SECOND-ORDER DIFFERENTIAL EQUATIONS

摘要

We study the periodic solutions of the second-order differential equations of the form x ± x~n = µf(t), or x± |x|~n = µf(t), where n = 4, 5,..., f(t) is a continuous T-periodic function such that ∫_0~T f(t)dt ≠ 0, and µ is a positive small parameter. Note that the differential equations x ± x~n = µf(t) are only continuous in t and smooth in x, and that the differential equations x ± |x|~n = µf(t) are only continuous in t and locally-Lipschitz in x.