Positive steady--states for two interacting species models with linear self-cross diffusions

In this paper, we discuss the positivesteady-state existence for predator-prey and competing interactionsystems between two species with linear self-cross diffusions. Themethods employed are the decomposing operators and the theory offixed point index on cones in a Banach space. We give sufficientconditions for the existence of positive solutions. The conditionsare given in terms of the signs of the principal eigenvalues ofcertain differential operators.

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