  We study the quasi-stationary behavior of multidimensional processes absorbed
when one of the coordinates vanishes. Our results cover competitive or weakly
cooperative Lotka-Volterra birth and death processes and Feller diffusions with
competitive Lotka-Volterra interaction. To this aim, we develop original
non-linear Lyapunov criteria involving two Lyapunov functions, which apply to
general Markov processes.
