This report studies the existence of non-constant solutions of certain two-point boundary value problems for 3-component systems with a small parameter C, under homogeneous Neumann conditions at the boundaries. This problem is related to the analysis of segregation patterns in population models of 3-competing and spatially dispersing species. It is shown that the reduced problem ( = 0) has many non-constant solutions exhibiting spatial segregation. Only a few of these, however, can serve as

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... d lowest-order approximations to solutions of the original problem when * is non-zero but small. A singular perturbation construc..ion clarifies which are in this category. The results of numerical computations of solutions are also illustrated.