Boundary blow-up solutions of cooperative systems

Louis Dupaigne; Olivier Goubet; Salomé Martínez; Juan Dávila

doi:10.1016/j.anihpc.2008.12.003

JournalsaihpcVol. 26, No. 5pp. 1767–1791

Boundary blow-up solutions of cooperative systems

Louis Dupaigne
LAMFA, CNRS UMR 6140, Université Picardie Jules Verne, 33, rue St Leu, 80039 Amiens, France
Olivier Goubet
LAMFA, CNRS UMR 6140, Université Picardie Jules Verne, 33, rue St Leu, 80039 Amiens, France
Salomé Martínez
Departamento de Ingeniería Matemática and CMM (CNRS UMI 2807), Universidad de Chile, Casilla 170/3, Correo 3, Santiago, Chile
Juan Dávila
Departamento de Ingeniería Matemática and CMM (CNRS UMI 2807), Universidad de Chile, Casilla 170/3, Correo 3, Santiago, Chile

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Abstract

We study the existence, uniqueness and boundary profile of nonnegative boundary blow-up solution to the cooperative system

⎩ ⎨ ⎧ Δ u = g (u - v) Δ v = f (v - β u) u = v = \infty in in on Ω, Ω, \partial Ω

in a smooth bounded domain of $R^{N}$ , where $f$ , $g$ are nondecreasing, nonnegative $C^{1}$ functions vanishing in $(- \infty, 0]$ and $β > 0$ is a parameter.

Cite this article

Louis Dupaigne, Olivier Goubet, Salomé Martínez, Juan Dávila, Boundary blow-up solutions of cooperative systems. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 5, pp. 1767–1791

DOI 10.1016/J.ANIHPC.2008.12.003