Singular Gierer–Meinhardt systems of elliptic boundary value problems

We establish existence results for singular Gierer–Meinhardt elliptic systems with zero Dirichlet boundary conditions. Gierer–Meinhardt systems are model problems for pattern formations of spatial tissue structures of morphogenesis. The mathematical difficulties are that the system becomes singular near the boundary and it is non-quasimonotone. We show the existence of positive solutions for the activator–inhibitor model with common sources.  2004 Elsevier Inc. All rights reserved