POSITIVE PERIODIC SOLUTIONS OF SECOND-ORDER DIFFERENTIAL EQUATIONS WITH SINGULARITIES

In this work, we consider the periodic boundary value problem {x '' + a(t)x = f(t, x) + c(t), x(0) = x(T), x'(0) = x'(T), where a, c is an element of L-1 (0, T) and f is a Caratheodory function. An existence theorem for positive periodic solutions is proved in the case where the associated Green function is nonnegative. Our result is valid for systems with strong singularities, and answers partially the open problem raised in Torres ['Weak singularities may help periodic solutions to exist', J Differential Equations 232 (2007), 277-284].