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Zbl 1074.35034
Pao, C.V.
Strongly coupled elliptic systems and applications to Lotka-Volterra models with cross-diffusion. (English)
[J] Nonlinear Anal., Theory Methods Appl. 60, No. 7, A, 1197-1217 (2005). ISSN 0362-546X

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.
[Yuri V. Rogovchenko (Famagusta)]

MSC 2000:: *35J55 Systems of elliptic equations, boundary value problems
35J65 (Nonlinear) BVP for (non)linear elliptic equations
35K57 Reaction-diffusion equations

Keywords: elliptic systems; reaction-diffusion systems; upper and lower solutions; monotone iterative method; positive solutions; quasisolutions

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