%0 Journal Article %T Solvability of a three-point nonlinear boundary-value problem %A Assia Guezane-Lakoud %A Smail Kelaiaia %J Electronic Journal of Differential Equations %D 2010 %I Texas State University %X Using the Leray Schauder nonlinear alternative, we prove the existence of a nontrivial solution for the three-point boundary-value problem $$displaylines{ u''+f(t,u)= 0,quad 0 %K Fixed point theorem %K three-point boundary-value problem %K non trivial solution %U http://ejde.math.txstate.edu/Volumes/2010/139/abstr.html