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

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  • In this paper, we discuss the positive steady-state existence for predator-prey and competing interaction systems between two species with linear self-cross diffusions. The methods employed are the decomposing operators and the theory of fixed point index on cones in a Banach space. We give sufficient conditions for the existence of positive solutions. The conditions are given in terms of the signs of the principal eigenvalues of certain differential operators.
    Mathematics Subject Classification: 35J60, 92D25.


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