  This paper deals with coexistence and extinction of time periodic
Volterra-Lotka type competing systems with nonlocal dispersal. Such issues have
already been studied for time independent systems with nonlocal dispersal and
time periodic systems with random dispersal, but have not been studied yet for
time periodic systems with nonlocal dispersal. In this paper, the relations
between the coefficients representing Malthusian growths, self regulations and
competitions of the two species have been obtained which ensure coexistence and
extinction for the time periodic Volterra-Lotka type system with nonlocal
dispersal. The underlying environment of the Volterra-Lotka type system under
consideration has either hostile surroundings, or non-flux boundary, or is
spatially periodic.
