T-PERIODIC SOLUTIONS FOR SOME 2ND-ORDER DIFFERENTIAL-EQUATIONS WITH SINGULARITIES

We study the existence of T-periodic positive solutions of the equation x" + f(t, x) = 0 where f(t, .) has a singularity of repulsive type near the origin. Under the assumption that f(t, x) lies between two lines of positive slope for large and positive x, we find a non-resonance condition which predicts the existence of one T-periodic solution. Our main result gives a Fredholm alternative-like result for the existence of T-periodic positive solutions for x" - 1/x(nu) + beta-x = h(t), nu greater-than-or-equal-to 1.