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Large solutions for an elliptic system of competitive type: existence, uniqueness and asymptotic behavior. (English) Zbl 1167.35373

Summary: This paper deals with the existence, uniqueness and asymptotic behavior of boundary blow-up solutions for an elliptic system of competitive type, where the weight functions \(a(x), b(x)\) vanish on the boundary of the underlying domain at different rates according to the point of the boundary. The proof relies on subsolutions and supersolutions, and the localization method.

MSC:

35J60 Nonlinear elliptic equations
35B25 Singular perturbations in context of PDEs
35B50 Maximum principles in context of PDEs
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