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Non-constant positive steady states for a strongly coupled nonlinear reaction-diffusion system arising in population dynamics. (English) Zbl 1335.35130

Summary: We consider a strongly coupled reaction-diffusion system describing three interacting species in a simple food chain structure. Based on the Leray-Schauder degree theory, the existence of non-constant positive steady states is investigated. The results indicate that, when the intrinsic growth rate of the middle species is small, cross-diffusions of the predators versus the preys are helpful to create global coexistence (stationary patterns).

MSC:

35K57 Reaction-diffusion equations
35B36 Pattern formations in context of PDEs
35B35 Stability in context of PDEs
92D25 Population dynamics (general)
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