Abstract
This work is concerned with the existence of entire solutions of the diffusive Lotka-Volterra competition system on the real line. We prove the existence of some entire solutions that are asymptotic, as t→−∞, to a traveling wave consisting of a single species. Depending on system parameters, these entire solutions evolve into two ore more stacked invasion waves as t→+∞. Our results cover both the weak and strong competition case. In the weak competition case, the existence of a class of entire solutions that forms a 4-dimensional manifold is proved.
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