Abstract
This paper is concerned with the spatial behavior of the strongly competing systems involving the square root of the Laplacian. The coexistence of minimal energy solutions is discussed and a mechanism to ensure coexistence is given. Moreover, in the case of two densities the global minimizer converges, as the interspecies interaction tends to infinity, to a spatially segregated distribution where the two densities coexist and solve a non-coupled variational problem.
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