@ARTICLE{Ams, author = { - Amster, Pablo - Cárdenas, Pedro P.} year = 2011-10-13 title = {Sturm-Liouville boundary conditions for a second order ODE.} abstract = {We study the semilinear second order ODE u00 + g(t, u) = 0 under the following Sturm- Liouville boundary condition au(0) + bu0(0) = u0 and cu(T) + du0(T) = uT . We obtain solutions by topological methods. Moreover, we show that a solution may be constructed recursively, under appropriate conditions.}