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

{Δu=g(uv)inΩ,Δv=f(vβu)inΩ,u=v=onΩ\left\{\begin{matrix} \mathrm{\Delta }u = g(u−v) & \text{in}\Omega , \\ \mathrm{\Delta }v = f(v−\beta u) & \text{in}\Omega , \\ u = v = \infty & \text{on}\partial \Omega \\ \end{matrix}\right.

in a smooth bounded domain of RN\mathbb{R}^{N}, where f, g are nondecreasing, nonnegative C1C^{1} functions vanishing in (−\infty ,0\right. and β>0\beta > 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