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Strongly coupled elliptic systems and applications to Lotka-Volterra models with cross-diffusion. (English) Zbl 1074.35034
The paper is concerned with the existence and method of construction of solutions for a general class of strongly coupled elliptic systems with three classical types of reaction functions that correspond to competition, prey-predator, and cooperating models. Application of the method of upper and lower solutions and associated monotone iterations lead to some positive solutions of the competition system and to quasisolutions of the predator-prey and cooperating systems. Sufficient conditions for the existence of a unique positive solution for each model are given.

35J55 Systems of elliptic equations, boundary value problems (MSC2000)
35J65 Nonlinear boundary value problems for linear elliptic equations
35K57 Reaction-diffusion equations
Full Text: DOI
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