Asymptotic behaviour of elliptic systems with mixed absorption and source terms

Article type: Research Article

Authors: Bidaut‐Véron, Marie‐Francoise^; | Grillot, Philippe

Affiliations: Laboratoire de Mathématiques et Physique Théorique, CNRS UPRES‐A 6083, Faculté des Sciences, Parc de Grandmont, 37200 Tours, France

Note: [] Corresponding author. Tel.: +33 2 47 36 72 60; Fax: +33 2 47 36 70 68; E‐mail: veronmf@univ‐tours.fr.

Abstract: We study the limit behaviour near the origin of the nonnegative solutions of the semilinear elliptic system \cases{ -\Delta u+\vert x\vert ^{a}v^{p}=0,\cr \Delta v+\vert x\vert ^{b}u^{q}=0,\cr}\quad \hbox{in}\ \mathbb{R}^{N}\ (N\geqslant 3), where p,q,a,b\in \mathbb{R}, with p,q>0, pq\neq 1. We give a priori estimates without any restriction on the values of p and q.

Journal: Asymptotic Analysis, vol. 19, no. 2, pp. 117-147, 1999