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Coexistence of two species in a strongly coupled cooperative model. (English) Zbl 1173.35711
Summary: The cooperative two-species Lotka-Volterra model is discussed. We study the existence of solutions to a elliptic system with homogeneous Dirichlet boundary conditions. Our results show that this problem possesses at least one coexistence state if the birth rates are big and self-diffusions and the intra-specific competitions are strong.

MSC:
35Q80 Applications of PDE in areas other than physics (MSC2000)
35J55 Systems of elliptic equations, boundary value problems (MSC2000)
35J60 Nonlinear elliptic equations
92D25 Population dynamics (general)
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