PERIODIC SOLUTIONS OF SOME CLASSES OF CONTINUOUS SECOND ORDER DIFFERENTIAL EQUATIONS

We study the periodic solutions of the second order differential equations of the form x +/- x(n) = mu f (t), or x +/- vertical bar x vertical bar(n) = mu f (t) where n = 4, 5,..., f (t) is a continuous T periodic function such that [GRAPHICS] f(t)dt not equal 0, and mu is a positive small parameter. Note that the differential equations x +/- x(n) = mu f (t) are only continuous in t and smooth in x, and that the differential equations x +/- vertical bar x vertical bar(n) = mu f (t) are only continuous in t and locally Lipschitz in x.