Abstract
We are concerned with the existence of positive solutions to the following boundary value problem in (0,infinity),1A>u ' u ' '=-a(t)u alpha,t>0, >A phi u ' u ' 0=0 andlimt ->+infinity u(t)=0, where alpha >= 0,phi is a nonnegative continuously differentiable function on 0,infinity, A is a continuous function on 0,infinity, differentiable, positive on 0,infinity and a is a nonnegative function satisfying some appropriate assumptions related to Karamata regular variation theory. We give also, estimates on such solutions.