%0 Journal Article %A Langa, J.A. %A Rodríguez Bernal, Aníbal %A Suárez, Antonio %T The sub-supertrajectory method. Application to the nonautonomous competition Lotka-Volterra model %D 2010 %@ 1575-9822 %U https://hdl.handle.net/20.500.14352/44757 %X In this paper we study in detail the pullback and forwards attractions to non-autonomous competition Lotka-Volterra system. In particular, under some conditions on the parameters, we prove the existence of a unique non-degenerate global solution for these models, which attracts any other complete bounded trajectory. For that we present the sub-supertrajectory tool as a generalization of the now classical subsupersolution method. %~