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Positive periodic solutions of Lotka-Volterra reaction-diffusion systems. (English) Zbl 0754.35065
(From the author’s abstract:) A general existence result of positive solutions in both components for the Lotka-Volterra R-D systems with time periodic and spatially dependent coefficients is given. Predator-prey, competing and cooperating interactions are included in the abstract framework. The fixed point index is used to prove the main result. Optimal coexistence results for the associated elliptic model subject to homogeneous Dirichlet boundary conditions and allowing the various coefficients in the model to be spatial dependent are also obtained.

35K57Reaction-diffusion equations
35B10Periodic solutions of PDE
35K50Systems of parabolic equations, boundary value problems (MSC2000)
35K60Nonlinear initial value problems for linear parabolic equations