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Two species of animals are competing or cooperating in the same environment. Under what conditions do they coexist peacefully? Or under what conditions does either one of the two species become extinct, that is, is either one of the two species excluded by the other? We investigate this phenomena in mathematical point of view. In this paper we concentrate on coexistence solutions of the competition or cooperation model

SMOOTH POSITIVE SOLUTIONS TO AN ELLIPTIC MODEL WITH $C^{2}$ FUNCTIONS