Abstract
Thepurposeofthispaper istogivesufficientconditionsfortheexistence anduniqueness of positive solutions toa rather general type of elliptic systemof the Dirichlet problemonaboundeddomainΩinRn. Also consideredare the effects of perturbationsonthecoexistencestateanduniqueness.Thetechniquesusedinthispaper aresuper-subsolutionsmethod,eigenvaluesofoperators,maximumprinciples, spectrum estimates, inverse functiontheory, andgeneral elliptictheory. Theargumentsalsorely onsomedetailedproperties forthesolutionof logisticequations. Theseresultsyieldan algebraicallycomputablecriterionforthepositivecoexistenceof speciesofanimalswith predator-preyrelationinmanybiologicalmodels.
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